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Calculated Shard: 34 (from laksa151)

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curl -X POST \
  'http://laksa034.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.electronics-tutorials.ws/resistor/res_3.html\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.electronics-tutorials.ws/resistor/res_3.html\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html","crawl_time":1775989180,"first_indexed_time":1518523071,"http_code":200,"src_unparsed":"ws,electronics-tutorials!www,\/resistor\/res_3.html s443","src_root_hash":"10833889916325664234","history_drop_reason":null,"meta_title":"Resistors in Series - Series Connected Resistors","meta_descriptions":["Electronics Tutorial about Resistors in Series and connected them together in series to form Potential or voltage divider networks"],"attrs_boilerpipe_text":"Connecting Resistors Together in Series\nIndividual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string.\nA resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and\/or the voltage allowing it to be used in voltage reference circuits and applications.\nResistors in series or complicated resistor networks can be replaced by one single equivalent resistor,\nR\nEQ\nor impedance,\nZ\nEQ\nand no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by\nOhm’s Law\nand\nKirchhoff’s Circuit Laws\n.\nResistors in Series\nResistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on.\nThen we can see that\nresistors in series\nhave a\nCommon Current\nflowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.\nThen the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:\nIn the following example the resistors\nR\n1\n,\nR\n2\nand\nR\n3\nare all connected together in series between points\nA\nand\nB\nwith a common current,\nI\nflowing through them.\nSeries Resistor Circuit\nAs the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance,\nR\nT\nof the circuit must be\nequal\nto the sum of all the individual resistors added together. That is\nand by taking the individual values of the resistors in our simple example above, the total equivalent resistance,\nR\nEQ\nis therefore given as:\nR\nEQ\n = R\n1\n + R\n2\n + R\n3\n = 1kΩ + 2kΩ + 6kΩ = 9kΩ\nSo we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of\n9kΩ\n.\nWhere four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit,\nR\nT\nwould still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value).\nThis total resistance is generally known as the\nEquivalent Resistance\nand can be defined as;  “\na single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit\n“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as:\nSeries Resistor Equation\nR\ntotal\n = R\n1\n + R\n2\n + R\n3\n + ….. R\nn\n etc.\nNote then that the total or equivalent resistance,\nR\nT\nhas the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.\nIf two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance,\nR\nT\nis equal to twice the value of one resistor. That is equal to\n2R\nand for three equal resistors in series,\n3R\n, etc.\nIf two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance,\nR\nT\nis equal to the mathematical sum of the two resistances. That is equal to\nR\n1\n + R\n2\n. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is:\nR\n1\n + R\n2\n + R\n3\n +…\n, etc.\nOne important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( \nR\nT\n ) of any two or more resistors connected together in series will always be\nGREATER\nthan the value of the largest resistor in the chain. In our example above \nR\nT\n = 9kΩ\nwhere as the largest value resistor is only\n6kΩ\n.\nSeries Resistor Voltage\nThe voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R\n1\n, R\n2\nand R\n3\n.\nV\nAB\n = V\nR1\n + V\nR2\n + V\nR3\n = 9V\n.\nUsing Ohm’s Law, the individual voltage drops across each resistor can be calculated as:\nThe voltage drop across resistor,\nR\n1\nis equal to: I*R\n1\n = 1mA x 1kΩ = 1V\nThe voltage drop across resistor,\nR\n2\nis equal to: I*R\n2\n = 1mA x 2kΩ = 2V\nThe voltage drop across resistor,\nR\n3\nis equal to: I*R\n3\n = 1mA x 6kΩ = 6V\nThus the voltage\nV\nAB\nbeing the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V.\nThe equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:\nThen series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having\nN\nresistive components will have N-different voltages across it while maintaining a common current.\nBy using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.\nResistors in Series Example No1\nUsing Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.\nAll the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.\nResistance\nCurrent\nVoltage\nPower\nR\n1\n= 10Ω\nI\n1\n= 200mA\nV\n1\n= 2V\nP\n1\n= 0.4W\nR\n2\n= 20Ω\nI\n2\n= 200mA\nV\n2\n= 4V\nP\n2\n= 0.8W\nR\n3\n= 30Ω\nI\n3\n= 200mA\nV\n3\n= 6V\nP\n3\n= 1.2W\nR\nT\n= 60Ω\nI\nT\n= 200mA\nV\nS\n= 12V\nP\nT\n= 2.4W\nThen for the circuit above,\nR\nT\n = 60Ω\n,\nI\nT\n = 200mA\n,\nV\nS\n = 12V\nand\nP\nT\n = 2.4W\nThe Voltage Divider Circuit\nWe can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a\nVoltage Divider Network\n.\nThis simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it.\nThe series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “\nthe supply voltage in a closed circuit is equal to the sum of all the voltage drops (I*R) around the circuit\n” and this can be used to good effect.\nThe\nVoltage Division Rule\n, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below.\nVoltage Divider Network\nThe circuit shown consists of just two resistors, R\n1\nand R\n2\nconnected together in series across the supply voltage V\nin\n. One side of the power supply voltage is connected to resistor, R\n1\n, and the voltage output, V\nout\nis taken from across resistor R\n2\n. The value of this output voltage is given by the corresponding formula.\nIf more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law\nI*R\n) values providing different but smaller voltage points from one single supply.\nSo if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below.\nThe\npotential divider circuit\nabove shows four resistances connected together is series. The voltage drop across points\nA\nand\nB\ncan be calculated using the potential divider formula as follows:\nWe can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both\nR2\nand\nR3\ntogether we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V).\nIn this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (R\nT\n) is equal to 100Ω or 100%, resistor R1 is 10% of R\nT\n. That is 10% of the source voltage V\nS\nwill appear across it, 20% of V\nS\nacross resistor R2, 30% across resistor R3, and 40% of the supply voltage V\nS\nacross resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this.\nNow lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage.\nConnecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor R\nL\nconnected in parallel across R\n2\nchanges the ratio of the two series resistances altering their voltage drop and this is demonstrated below.\nResistors in Series Example No2\nCalculate the voltage drops across X and Y\na) Without\nR\nL\nconnected\nb) With\nR\nL\nconnected\nAs you can see from above, the output voltage\nV\nout\nwithout the load resistor connected gives us the required output voltage of 6V but the same output voltage at\nV\nout\nwhen the load is connected drops to only 4V, (\nResistors in Parallel\n).\nThen we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage V\nout\nis determined by the ratio of R\n1\nto R\n2\n. However, as the load resistance, R\nL\nincreases towards infinity (\n∞\n) this loading effect reduces and the voltage ratio of\nVout\/Vs\nbecomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output.\nThe effect of reducing a signal or voltage level is known as\nAttenuation\nso care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction.\nA variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control.\nThe\nVoltage Divider Circuit\nis the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer.\nAs well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems.\nApplications of Resistors in Series\nWe have seen that\nResistors in Series\ncan be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network.\nIf we replace one of the resistors in the voltage divider circuit above with a\nSensor\nsuch as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.\nFor example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.\nThermistor Circuit\nAt 25°C\nAt 100°C\nSo by changing the fixed\n1KΩ\nresistor,\nR\n2\nin our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.\nResistors in Series Summary\nTo summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series.\nResistors in Series\ncarry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = I*R ). Then series circuits are voltage dividers.\nIn a series resistor network the individual resistors add together to give an equivalent resistance, ( R\nT\n) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.\nIn the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.","attrs_markdown":"[![Electronics Tutorials White Logo](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/etuts-lg-white.png)](https:\/\/www.electronics-tutorials.ws\/) [X](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html)\n\n[![Electronics Tutorials Logo](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/main-logo.png?fit=218,35)](https:\/\/www.electronics-tutorials.ws\/)\n\n[Register to download premium content\\!](https:\/\/www.electronics-tutorials.ws\/register)\n\n[![Electronics Tutorials 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[Contact Us](https:\/\/www.electronics-tutorials.ws\/contact)\n\nAdvertisement\n\n[Home](https:\/\/www.electronics-tutorials.ws\/ \"Back Home\") \/ [Resistors](https:\/\/www.electronics-tutorials.ws\/category\/resistor \"Resistors Section\") \/ Resistors in Series\n\n![Resistors in Series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2013\/08\/res7.gif?fit=501%2C140?fit=355,226)\n\n# Resistors in Series\nResistors are said to be connected in series when they are daisy chained together in a single line resulting in a common current flowing through them\n\n## Connecting Resistors Together in Series\nIndividual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string.\n\nA resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and\/or the voltage allowing it to be used in voltage reference circuits and applications.\n\nResistors in series or complicated resistor networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by [Ohm’s Law](https:\/\/www.electronics-tutorials.ws\/dccircuits\/dcp_2.html) and [Kirchhoff’s Circuit Laws](https:\/\/www.electronics-tutorials.ws\/dccircuits\/dcp_4.html).\n\n## Resistors in Series\nResistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on.\n\nThen we can see that *resistors in series* have a **Common Current** flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.\n\nThen the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:\n\n![series resistor current](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res43.gif)\n\nIn the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them.\n\n### Series Resistor Circuit\n![resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res7.gif)\n\nAs the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be **equal** to the sum of all the individual resistors added together. That is\n\n![series resistance equation](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res44.gif)\n\nand by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as:\n\nREQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ\n\n![series resistors equivalent resistance](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res46.gif)\n\nSo we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ.\n\nWhere four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value).\n\nThis total resistance is generally known as the **Equivalent Resistance** and can be defined as; “*a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit*“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as:\n\n### Series Resistor Equation\nRtotal = R1 + R2 + R3 + ….. Rn etc.\n\nNote then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.\n\n|   |   |\n|---|---|\n| ![equal resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res74.gif) | If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc. |\n\n|   |   |\n|---|---|\n| ![unequal resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res75.gif) | If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc. |\n\nOne important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be **GREATER** than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ.\n\n## Series Resistor Voltage\nThe voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1, R2 and R3.\n\nVAB = VR1 + VR2 + VR3 = 9V.\n\nUsing Ohm’s Law, the individual voltage drops across each resistor can be calculated as:\n\nThe voltage drop across resistor, R1 is equal to: I\\*R1 = 1mA x 1kΩ = 1V\n\nThe voltage drop across resistor, R2 is equal to: I\\*R2 = 1mA x 2kΩ = 2V\n\nThe voltage drop across resistor, R3 is equal to: I\\*R3 = 1mA x 6kΩ = 6V\n\nThus the voltage VAB being the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V.\n\nThe equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:\n\n![series resistor voltages](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res45.gif)\n\nThen series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having *N* resistive components will have N-different voltages across it while maintaining a common current.\n\nBy using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.\n\n## Resistors in Series Example No1\nUsing Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.\n\n![resistors in series circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res47.gif)\n\nAll the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.\n\n|   |   |   |   |\n|---|---|---|---|\n| Resistance | Current | Voltage | Power |\n| R1 = 10Ω | I1 = 200mA | V1 = 2V | P1 = 0.4W |\n| R2 = 20Ω | I2 = 200mA | V2 = 4V | P2 = 0.8W |\n| R3 = 30Ω | I3 = 200mA | V3 = 6V | P3 = 1.2W |\n| RT = 60Ω | IT = 200mA | VS = 12V | PT = 2.4W |\n\nThen for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W\n\n## The Voltage Divider Circuit\nWe can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a **Voltage Divider Network**.\n\nThis simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it.\n\nThe series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “*the supply voltage in a closed circuit is equal to the sum of all the voltage drops (I\\*R) around the circuit*” and this can be used to good effect.\n\nThe **Voltage Division Rule**, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below.\n\n### Voltage Divider Network\n![voltage divider network](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res10.gif)\n\nThe circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula.\n\nIf more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law **I\\*R**) values providing different but smaller voltage points from one single supply.\n\nSo if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below.\n\n![series divider circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/articles-divider8.gif)\n\nThe *potential divider circuit* above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows:\n\n![voltage divider formula](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/articles-divider9.gif)\n\nWe can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V).\n\nIn this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) is equal to 100Ω or 100%, resistor R1 is 10% of RT. That is 10% of the source voltage VS will appear across it, 20% of VS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this.\n\nNow lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage.\n\nConnecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below.\n\n## Resistors in Series Example No2\n**Calculate the voltage drops across X and Y**\n\na) Without RL connected\n\nb) With RL connected\n\n![potential divider network](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res15.gif)\n\nAs you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, ([Resistors in Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_4.html)).\n\nThen we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio of Vout\/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output.\n\nThe effect of reducing a signal or voltage level is known as **Attenuation** so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction.\n\nA variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control.\n\nThe **Voltage Divider Circuit** is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer.\n\nAs well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems.\n\n## Applications of Resistors in Series\nWe have seen that **Resistors in Series** can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network.\n\nIf we replace one of the resistors in the voltage divider circuit above with a *Sensor* such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.\n\nFor example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.\n\n### Thermistor Circuit\n![thermistor circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res16.gif)\n\nAt 25°C\n\n![temperature at 25 degs](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res17.gif)\n\nAt 100°C\n\n![temperature at 100 degs](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res18.gif)\n\nSo by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.\n\n## Resistors in Series Summary\nTo summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. **Resistors in Series** carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = I\\*R ). Then series circuits are voltage dividers.\n\nIn a series resistor network the individual resistors add together to give an equivalent resistance, ( RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.\n\nIn the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.\n\n[![previous](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/arrow_alt_left_inv.png)Previous Resistor Colour Code](https:\/\/www.electronics-tutorials.ws\/resistor\/res_2.html)\n\n[Next Resistors in Parallel![next](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/arrow_alt_right_inv.png)](https:\/\/www.electronics-tutorials.ws\/resistor\/res_4.html)\n\n## Read more Tutorials inResistors\n- [1\\. Types of Resistor](https:\/\/www.electronics-tutorials.ws\/resistor\/res_1.html)\n- [2\\. Resistor Colour Code](https:\/\/www.electronics-tutorials.ws\/resistor\/res_2.html)\n- [3\\. Resistors in Series](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html)\n- [4\\. Resistors in Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_4.html)\n- [5\\. Resistors in Series and Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_5.html)\n- [6\\. Potential Difference](https:\/\/www.electronics-tutorials.ws\/resistor\/res_6.html)\n- [7\\. Resistor Power Rating](https:\/\/www.electronics-tutorials.ws\/resistor\/res_7.html)\n- [8\\. Resistors in AC Circuits](https:\/\/www.electronics-tutorials.ws\/resistor\/res_8.html)\n- [9\\. Resistor Tutorial Summary](https:\/\/www.electronics-tutorials.ws\/resistor\/res_9.html)\n- [10\\. Varistor Tutorial](https:\/\/www.electronics-tutorials.ws\/resistor\/varistor.html)\n- [11\\. Resistor Colour Code Wheel](https:\/\/www.electronics-tutorials.ws\/resistor\/resistor-colour-code-wheel.html)\n- [12\\. Potentiometers](https:\/\/www.electronics-tutorials.ws\/resistor\/potentiometer.html)\n- [13\\. Resistivity](https:\/\/www.electronics-tutorials.ws\/resistor\/resistivity.html)\n- [14\\. LED Resistor](https:\/\/www.electronics-tutorials.ws\/resistor\/led-resistor.html)\n\n## 133 Comments\n###\n## Join the conversation\n[Cancel reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#respond)\n\nError! Please fill all fields.\n\n- Thabelang\n  \n  I really like this .\n  \n  Posted on [April 01st 2025 \\| 10:56 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-101659)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=101659#respond)\n- Val Jardiolin\n  \n  hello\n  \n  Posted on [November 18th 2024 \\| 6:01 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-90995)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=90995#respond)\n- Steven Lingling\n  \n  Net Voltage of series connected resistance 3 ohms 2 ohms and 5 ohms with 3 ohms Voltage across terminals is 6 volts.\n  \n  Posted on [August 24th 2024 \\| 2:31 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-89989)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=89989#respond)\n- MAKGOPELO\n  \n  This document is helpful\n  \n  Posted on [February 26th 2024 \\| 4:49 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-87504)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=87504#respond)\n- Mohamed Abdelfatah\n  \n  reduce current in an electric circuit, a resistor R should be connected in the circuit. In this case R will be\n  \n  Posted on [July 20th 2023 \\| 3:39 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-84441)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=84441#respond)\n- Abu Chernor kargbo\n  \n  I need help to you guys by helping me solve problems on Electric circuit and Electronics\n  \n  Posted on [January 30th 2023 \\| 1:02 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-82047)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=82047#respond)\n- Jackey\n  \n  Thanks you\\!\n  \n  Posted on [January 06th 2023 \\| 1:40 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-81741)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=81741#respond)\n- Emmanuel Ackon\n  \n  I went to know how resistance how to opposite the flow of electric current in a circuit, through in circuit dergem\n  \n  Posted on [November 19th 2022 \\| 8:05 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-81157)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=81157#respond)\n- MUSA BAWA\n  \n  Am very happy with site\n  \n  Posted on [September 29th 2022 \\| 11:11 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-80669)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=80669#respond)\n- Fazlullahkhanfazlullah\n  \n  I need this book\n  \n  Posted on [May 27th 2022 \\| 7:32 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-79293)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=79293#respond)\n- Don mulenga\n  \n  Hey I want to know about it\n  \n  Posted on [April 26th 2022 \\| 8:08 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-78774)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=78774#respond)\n- Tasiu\n  \n  I need tutorial\n  \n  Posted on [March 15th 2022 \\| 6:23 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-77935)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=77935#respond)\n- Pius\n  \n  IAMcame because I like it\n  \n  Posted on [March 03rd 2022 \\| 7:29 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-77689)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=77689#respond)\n- Ayele endeshaw\n  \n  thnk you\n  \n  Posted on [February 21st 2022 \\| 7:26 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-77473)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=77473#respond)\n- Isreal Emmanuel\n  \n  Nice\n  \n  Posted on [February 07th 2022 \\| 9:27 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-77304)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=77304#respond)\n- marema joel\n  \n  yes I like to read and learn more about electronic circuits to know about electrical circuit calculation I want to learn school more\n  \n  Posted on [November 29th 2021 \\| 9:27 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-76458)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=76458#respond)\n- Aaron M Jacobs\n  \n  Want to be part\n  \n  Posted on [September 29th 2021 \\| 10:54 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-75931)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=75931#respond)\n- Himanshu Parashar\n  \n  True false\n  \n  Posted on [August 08th 2021 \\| 11:43 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-75395)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=75395#respond)\n- Dauda lucky mangai\n  \n  Draw a circuit with a mixemum series of 5\n  \n  Posted on [July 12th 2021 \\| 4:13 pm](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-75106)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=75106#respond)\n- Kaliza Misheck\n  \n  They is sense in these notes and very easy to understand.i love this\n  \n  Posted on [March 07th 2021 \\| 4:27 am](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html#comment-73212)\n  \n  [Reply](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html?replytocom=73212#respond)\n\n[View More](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html\/comment-page-2#comments)\n\n![Loading](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/loading.gif)\n\n## Read more Tutorials inResistors\n- [1\\. Types of Resistor](https:\/\/www.electronics-tutorials.ws\/resistor\/res_1.html)\n- [2\\. Resistor Colour Code](https:\/\/www.electronics-tutorials.ws\/resistor\/res_2.html)\n- [3\\. Resistors in Series](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html)\n- [4\\. Resistors in Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_4.html)\n- [5\\. Resistors in Series and Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_5.html)\n- [6\\. Potential Difference](https:\/\/www.electronics-tutorials.ws\/resistor\/res_6.html)\n- [7\\. Resistor Power Rating](https:\/\/www.electronics-tutorials.ws\/resistor\/res_7.html)\n- [8\\. Resistors in AC Circuits](https:\/\/www.electronics-tutorials.ws\/resistor\/res_8.html)\n- [9\\. Resistor Tutorial Summary](https:\/\/www.electronics-tutorials.ws\/resistor\/res_9.html)\n- [10\\. Varistor Tutorial](https:\/\/www.electronics-tutorials.ws\/resistor\/varistor.html)\n- [11\\. Resistor Colour Code Wheel](https:\/\/www.electronics-tutorials.ws\/resistor\/resistor-colour-code-wheel.html)\n- [12\\. Potentiometers](https:\/\/www.electronics-tutorials.ws\/resistor\/potentiometer.html)\n- [13\\. Resistivity](https:\/\/www.electronics-tutorials.ws\/resistor\/resistivity.html)\n- [14\\. LED Resistor](https:\/\/www.electronics-tutorials.ws\/resistor\/led-resistor.html)\n\nAdvertisement\n\nAdvertisement\n\n[Close](https:\/\/www.electronics-tutorials.ws\/resistor\/res_3.html)\n\n- [The Basics]()\n  - [Contact Us](https:\/\/www.electronics-tutorials.ws\/contact)\n  - [Privacy Policy](https:\/\/www.aspencore.com\/privacy-policy)\n  - [Terms of Use](https:\/\/www.aspencore.com\/terms-of-use)\n- [For Advertisers]()\n  - [Contact Sales](https:\/\/aspencore.com\/contact)\n  - [Media Guide Request](https:\/\/aspencore.com\/media-guide-request)\n- [Aspencore Network]()\n  - [EDN](https:\/\/www.edn.com\/)\n  - [EE Times](https:\/\/www.eetimes.com\/)\n  - [EEWeb](https:\/\/www.eeweb.com\/)\n  - [Electronic Products](https:\/\/www.electronicproducts.com\/)\n  - [Power Electronics News](https:\/\/www.powerelectronicsnews.com\/)\n  - [Embedded](https:\/\/www.embedded.com\/)\n  - [Planet Analog](https:\/\/www.planetanalog.com\/)\n  - [TechOnline](https:\/\/www.techonline.com\/)\n  - [Electronics Know How](https:\/\/electronics-know-how.com\/)\n- [Global Network]()\n  - [EE Times Asia](https:\/\/www.eetasia.com\/)\n  - [EE Times China](https:\/\/www.eet-china.com\/)\n  - [EE Times India](https:\/\/www.eetindia.co.in\/)\n  - [EE Times Japan](https:\/\/eetimes.jp\/)\n  - [EE Times Taiwan](https:\/\/www.eettaiwan.com\/)\n  - [EDN Asia](https:\/\/www.ednasia.com\/)\n  - [EDN China](https:\/\/www.ednchina.com\/)\n  - [EDN Taiwan](https:\/\/www.edntaiwan.com\/)\n  - [EDN Japan](https:\/\/ednjapan.com\/)\n  - [ESM China](https:\/\/www.esmchina.com\/)\n- [Connect with Us]()\n  - [Facebook](https:\/\/www.facebook.com\/electronicstutorials)\n\n![AspenCore logo general](https:\/\/www.electronics-tutorials.ws\/wp-content\/themes\/electronics-tutorials-v2\/img\/AspenCore_logo.png?fit=140,34)\n\nAll contents are Copyright © 2026 by AspenCore, Inc. All rights reserved.\n\n![Quantcast](https:\/\/pixel.quantserve.com\/pixel\/p-ha81gRQTKQ0vn.gif)","attrs_readable_markdown":"## Connecting Resistors Together in Series\nIndividual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string.\n\nA resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and\/or the voltage allowing it to be used in voltage reference circuits and applications.\n\nResistors in series or complicated resistor networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by [Ohm’s Law](https:\/\/www.electronics-tutorials.ws\/dccircuits\/dcp_2.html) and [Kirchhoff’s Circuit Laws](https:\/\/www.electronics-tutorials.ws\/dccircuits\/dcp_4.html).\n\n## Resistors in Series\nResistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on.\n\nThen we can see that *resistors in series* have a **Common Current** flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.\n\nThen the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:\n\n![series resistor current](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res43.gif)\n\nIn the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them.\n\n### Series Resistor Circuit\n![resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res7.gif)\n\nAs the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be **equal** to the sum of all the individual resistors added together. That is\n\n![series resistance equation](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res44.gif)\n\nand by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as:\n\nREQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ\n\n![series resistors equivalent resistance](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res46.gif)\n\nSo we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ.\n\nWhere four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value).\n\nThis total resistance is generally known as the **Equivalent Resistance** and can be defined as; “*a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit*“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as:\n\n### Series Resistor Equation\nRtotal = R1 + R2 + R3 + ….. Rn etc.\n\nNote then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.\n\n|   |   |\n|---|---|\n| ![equal resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res74.gif) | If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc. |\n\n|   |   |\n|---|---|\n| ![unequal resistors in series](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res75.gif) | If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc. |\n\nOne important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be **GREATER** than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ.\n\n## Series Resistor Voltage\nThe voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1, R2 and R3.\n\nVAB = VR1 + VR2 + VR3 = 9V.\n\nUsing Ohm’s Law, the individual voltage drops across each resistor can be calculated as:\n\nThe voltage drop across resistor, R1 is equal to: I\\*R1 = 1mA x 1kΩ = 1V\n\nThe voltage drop across resistor, R2 is equal to: I\\*R2 = 1mA x 2kΩ = 2V\n\nThe voltage drop across resistor, R3 is equal to: I\\*R3 = 1mA x 6kΩ = 6V\n\nThus the voltage VAB being the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V.\n\nThe equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:\n\n![series resistor voltages](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res45.gif)\n\nThen series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having *N* resistive components will have N-different voltages across it while maintaining a common current.\n\nBy using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.\n\n## Resistors in Series Example No1\nUsing Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.\n\n![resistors in series circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res47.gif)\n\nAll the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.\n\n|   |   |   |   |\n|---|---|---|---|\n| Resistance | Current | Voltage | Power |\n| R1 = 10Ω | I1 = 200mA | V1 = 2V | P1 = 0.4W |\n| R2 = 20Ω | I2 = 200mA | V2 = 4V | P2 = 0.8W |\n| R3 = 30Ω | I3 = 200mA | V3 = 6V | P3 = 1.2W |\n| RT = 60Ω | IT = 200mA | VS = 12V | PT = 2.4W |\n\nThen for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W\n\n## The Voltage Divider Circuit\nWe can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a **Voltage Divider Network**.\n\nThis simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it.\n\nThe series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “*the supply voltage in a closed circuit is equal to the sum of all the voltage drops (I\\*R) around the circuit*” and this can be used to good effect.\n\nThe **Voltage Division Rule**, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below.\n\n### Voltage Divider Network\n![voltage divider network](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res10.gif)\n\nThe circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula.\n\nIf more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law **I\\*R**) values providing different but smaller voltage points from one single supply.\n\nSo if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below.\n\n![series divider circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/articles-divider8.gif)\n\nThe *potential divider circuit* above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows:\n\n![voltage divider formula](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/articles-divider9.gif)\n\nWe can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V).\n\nIn this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) is equal to 100Ω or 100%, resistor R1 is 10% of RT. That is 10% of the source voltage VS will appear across it, 20% of VS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this.\n\nNow lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage.\n\nConnecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below.\n\n## Resistors in Series Example No2\n**Calculate the voltage drops across X and Y**\n\na) Without RL connected\n\nb) With RL connected\n\n![potential divider network](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res15.gif)\n\nAs you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, ([Resistors in Parallel](https:\/\/www.electronics-tutorials.ws\/resistor\/res_4.html)).\n\nThen we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio of Vout\/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output.\n\nThe effect of reducing a signal or voltage level is known as **Attenuation** so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction.\n\nA variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control.\n\nThe **Voltage Divider Circuit** is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer.\n\nAs well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems.\n\n## Applications of Resistors in Series\nWe have seen that **Resistors in Series** can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network.\n\nIf we replace one of the resistors in the voltage divider circuit above with a *Sensor* such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.\n\nFor example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.\n\n### Thermistor Circuit\n![thermistor circuit](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res16.gif)\n\nAt 25°C\n\n![temperature at 25 degs](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res17.gif)\n\nAt 100°C\n\n![temperature at 100 degs](https:\/\/www.electronics-tutorials.ws\/wp-content\/uploads\/2018\/05\/resistor-res18.gif)\n\nSo by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.\n\n## Resistors in Series Summary\nTo summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. **Resistors in Series** carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = I\\*R ). Then series circuits are voltage dividers.\n\nIn a series resistor network the individual resistors add together to give an equivalent resistance, ( RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.\n\nIn the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.","meta_canonical":null}

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Boilerpipe Text	Connecting Resistors Together in Series Individual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string. A resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and/or the voltage allowing it to be used in voltage reference circuits and applications. Resistors in series or complicated resistor networks can be replaced by one single equivalent resistor, R EQ or impedance, Z EQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by Ohm’s Law and Kirchhoff’s Circuit Laws . Resistors in Series Resistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then we can see that resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path. Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example: In the following example the resistors R 1 , R 2 and R 3 are all connected together in series between points A and B with a common current, I flowing through them. Series Resistor Circuit As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, R T of the circuit must be equal to the sum of all the individual resistors added together. That is and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, R EQ is therefore given as: R EQ = R 1 + R 2 + R 3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ . Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, R T would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value). This total resistance is generally known as the Equivalent Resistance and can be defined as; “ a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit “. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as: Series Resistor Equation R total = R 1 + R 2 + R 3 + ….. R n etc. Note then that the total or equivalent resistance, R T has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances. If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, R T is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R , etc. If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, R T is equal to the mathematical sum of the two resistances. That is equal to R 1 + R 2 . If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R 1 + R 2 + R 3 +… , etc. One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( R T ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above R T = 9kΩ where as the largest value resistor is only 6kΩ . Series Resistor Voltage The voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R 1 , R 2 and R 3 . V AB = V R1 + V R2 + V R3 = 9V . Using Ohm’s Law, the individual voltage drops across each resistor can be calculated as: The voltage drop across resistor, R 1 is equal to: IR 1 = 1mA x 1kΩ = 1V The voltage drop across resistor, R 2 is equal to: IR 2 = 1mA x 2kΩ = 2V The voltage drop across resistor, R 3 is equal to: IR 3 = 1mA x 6kΩ = 6V Thus the voltage V AB being the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V. The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as: Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N resistive components will have N-different voltages across it while maintaining a common current. By using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor. Resistors in Series Example No1 Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit. All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form. Resistance Current Voltage Power R 1 = 10Ω I 1 = 200mA V 1 = 2V P 1 = 0.4W R 2 = 20Ω I 2 = 200mA V 2 = 4V P 2 = 0.8W R 3 = 30Ω I 3 = 200mA V 3 = 6V P 3 = 1.2W R T = 60Ω I T = 200mA V S = 12V P T = 2.4W Then for the circuit above, R T = 60Ω , I T = 200mA , V S = 12V and P T = 2.4W The Voltage Divider Circuit We can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a Voltage Divider Network . This simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it. The series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “ the supply voltage in a closed circuit is equal to the sum of all the voltage drops (IR) around the circuit ” and this can be used to good effect. The Voltage Division Rule , allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below. Voltage Divider Network The circuit shown consists of just two resistors, R 1 and R 2 connected together in series across the supply voltage V in . One side of the power supply voltage is connected to resistor, R 1 , and the voltage output, V out is taken from across resistor R 2 . The value of this output voltage is given by the corresponding formula. If more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law IR ) values providing different but smaller voltage points from one single supply. So if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below. The potential divider circuit above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows: We can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V). In this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (R T ) is equal to 100Ω or 100%, resistor R1 is 10% of R T . That is 10% of the source voltage V S will appear across it, 20% of V S across resistor R2, 30% across resistor R3, and 40% of the supply voltage V S across resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this. Now lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage. Connecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor R L connected in parallel across R 2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below. Resistors in Series Example No2 Calculate the voltage drops across X and Y a) Without R L connected b) With R L connected As you can see from above, the output voltage V out without the load resistor connected gives us the required output voltage of 6V but the same output voltage at V out when the load is connected drops to only 4V, ( Resistors in Parallel ). Then we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage V out is determined by the ratio of R 1 to R 2 . However, as the load resistance, R L increases towards infinity ( ∞ ) this loading effect reduces and the voltage ratio of Vout/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output. The effect of reducing a signal or voltage level is known as Attenuation so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction. A variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control. The Voltage Divider Circuit is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer. As well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems. Applications of Resistors in Series We have seen that Resistors in Series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If we replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured. For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures. Thermistor Circuit At 25°C At 100°C So by changing the fixed 1KΩ resistor, R 2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range. Resistors in Series Summary To summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. Resistors in Series carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = IR ). Then series circuits are voltage dividers. In a series resistor network the individual resistors add together to give an equivalent resistance, ( R T ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit. In the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.
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[Contact Us](https://www.electronics-tutorials.ws/contact) Advertisement [Home](https://www.electronics-tutorials.ws/ "Back Home") / [Resistors](https://www.electronics-tutorials.ws/category/resistor "Resistors Section") / Resistors in Series ![Resistors in Series](https://www.electronics-tutorials.ws/wp-content/uploads/2013/08/res7.gif?fit=501%2C140?fit=355,226) # Resistors in Series Resistors are said to be connected in series when they are daisy chained together in a single line resulting in a common current flowing through them ## Connecting Resistors Together in Series Individual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string. A resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and/or the voltage allowing it to be used in voltage reference circuits and applications. Resistors in series or complicated resistor networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by [Ohm’s Law](https://www.electronics-tutorials.ws/dccircuits/dcp_2.html) and [Kirchhoff’s Circuit Laws](https://www.electronics-tutorials.ws/dccircuits/dcp_4.html). ## Resistors in Series Resistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then we can see that resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path. Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example: ![series resistor current](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res43.gif) In the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them. ### Series Resistor Circuit ![resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res7.gif) As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is ![series resistance equation](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res44.gif) and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as: REQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ ![series resistors equivalent resistance](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res46.gif) So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ. Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value). This total resistance is generally known as the Equivalent Resistance and can be defined as; “a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as: ### Series Resistor Equation Rtotal = R1 + R2 + R3 + ….. Rn etc. Note then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances. \| \| \| \|---\|---\| \| ![equal resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res74.gif) \| If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc. \| \| \| \| \|---\|---\| \| ![unequal resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res75.gif) \| If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc. \| One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ. ## Series Resistor Voltage The voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1, R2 and R3. VAB = VR1 + VR2 + VR3 = 9V. Using Ohm’s Law, the individual voltage drops across each resistor can be calculated as: The voltage drop across resistor, R1 is equal to: I\R1 = 1mA x 1kΩ = 1V The voltage drop across resistor, R2 is equal to: I\R2 = 1mA x 2kΩ = 2V The voltage drop across resistor, R3 is equal to: I\R3 = 1mA x 6kΩ = 6V Thus the voltage VAB being the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V. The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as: ![series resistor voltages](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res45.gif) Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N* resistive components will have N-different voltages across it while maintaining a common current. By using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor. ## Resistors in Series Example No1 Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit. ![resistors in series circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res47.gif) All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form. \| \| \| \| \| \|---\|---\|---\|---\| \| Resistance \| Current \| Voltage \| Power \| \| R1 = 10Ω \| I1 = 200mA \| V1 = 2V \| P1 = 0.4W \| \| R2 = 20Ω \| I2 = 200mA \| V2 = 4V \| P2 = 0.8W \| \| R3 = 30Ω \| I3 = 200mA \| V3 = 6V \| P3 = 1.2W \| \| RT = 60Ω \| IT = 200mA \| VS = 12V \| PT = 2.4W \| Then for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W ## The Voltage Divider Circuit We can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a Voltage Divider Network. This simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it. The series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “the supply voltage in a closed circuit is equal to the sum of all the voltage drops (I\R) around the circuit” and this can be used to good effect. The Voltage Division Rule, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below. ### Voltage Divider Network ![voltage divider network](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res10.gif) The circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula. If more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law I\R*) values providing different but smaller voltage points from one single supply. So if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below. ![series divider circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/articles-divider8.gif) The potential divider circuit* above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows: ![voltage divider formula](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/articles-divider9.gif) We can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V). In this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) is equal to 100Ω or 100%, resistor R1 is 10% of RT. That is 10% of the source voltage VS will appear across it, 20% of VS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this. Now lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage. Connecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below. ## Resistors in Series Example No2 Calculate the voltage drops across X and Y a) Without RL connected b) With RL connected ![potential divider network](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res15.gif) As you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, ([Resistors in Parallel](https://www.electronics-tutorials.ws/resistor/res_4.html)). Then we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio of Vout/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output. The effect of reducing a signal or voltage level is known as Attenuation so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction. A variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control. The Voltage Divider Circuit is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer. As well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems. ## Applications of Resistors in Series We have seen that Resistors in Series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If we replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured. For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures. ### Thermistor Circuit ![thermistor circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res16.gif) At 25°C ![temperature at 25 degs](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res17.gif) At 100°C ![temperature at 100 degs](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res18.gif) So by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range. ## Resistors in Series Summary To summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. Resistors in Series carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = I\*R ). Then series circuits are voltage dividers. In a series resistor network the individual resistors add together to give an equivalent resistance, ( RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit. In the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit. [![previous](https://www.electronics-tutorials.ws/wp-content/themes/electronics-tutorials-v2/img/arrow_alt_left_inv.png)Previous Resistor Colour Code](https://www.electronics-tutorials.ws/resistor/res_2.html) [Next Resistors in Parallel![next](https://www.electronics-tutorials.ws/wp-content/themes/electronics-tutorials-v2/img/arrow_alt_right_inv.png)](https://www.electronics-tutorials.ws/resistor/res_4.html) ## Read more Tutorials inResistors - [1\. Types of Resistor](https://www.electronics-tutorials.ws/resistor/res_1.html) - [2\. Resistor Colour Code](https://www.electronics-tutorials.ws/resistor/res_2.html) - [3\. Resistors in Series](https://www.electronics-tutorials.ws/resistor/res_3.html) - [4\. Resistors in Parallel](https://www.electronics-tutorials.ws/resistor/res_4.html) - [5\. Resistors in Series and Parallel](https://www.electronics-tutorials.ws/resistor/res_5.html) - [6\. Potential Difference](https://www.electronics-tutorials.ws/resistor/res_6.html) - [7\. Resistor Power Rating](https://www.electronics-tutorials.ws/resistor/res_7.html) - [8\. Resistors in AC Circuits](https://www.electronics-tutorials.ws/resistor/res_8.html) - [9\. Resistor Tutorial Summary](https://www.electronics-tutorials.ws/resistor/res_9.html) - [10\. Varistor Tutorial](https://www.electronics-tutorials.ws/resistor/varistor.html) - [11\. Resistor Colour Code Wheel](https://www.electronics-tutorials.ws/resistor/resistor-colour-code-wheel.html) - [12\. Potentiometers](https://www.electronics-tutorials.ws/resistor/potentiometer.html) - [13\. Resistivity](https://www.electronics-tutorials.ws/resistor/resistivity.html) - [14\. LED Resistor](https://www.electronics-tutorials.ws/resistor/led-resistor.html) ## 133 Comments ### ## Join the conversation [Cancel reply](https://www.electronics-tutorials.ws/resistor/res_3.html#respond) Error! Please fill all fields. - Thabelang I really like this . Posted on [April 01st 2025 \\| 10:56 am](https://www.electronics-tutorials.ws/resistor/res_3.html#comment-101659) [Reply](https://www.electronics-tutorials.ws/resistor/res_3.html?replytocom=101659#respond) - Val Jardiolin hello Posted on [November 18th 2024 \\| 6:01 am](https://www.electronics-tutorials.ws/resistor/res_3.html#comment-90995) [Reply](https://www.electronics-tutorials.ws/resistor/res_3.html?replytocom=90995#respond) - Steven Lingling Net Voltage of series connected resistance 3 ohms 2 ohms and 5 ohms with 3 ohms Voltage across terminals is 6 volts. 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Types of Resistor](https://www.electronics-tutorials.ws/resistor/res_1.html) - [2\. Resistor Colour Code](https://www.electronics-tutorials.ws/resistor/res_2.html) - [3\. Resistors in Series](https://www.electronics-tutorials.ws/resistor/res_3.html) - [4\. Resistors in Parallel](https://www.electronics-tutorials.ws/resistor/res_4.html) - [5\. Resistors in Series and Parallel](https://www.electronics-tutorials.ws/resistor/res_5.html) - [6\. Potential Difference](https://www.electronics-tutorials.ws/resistor/res_6.html) - [7\. Resistor Power Rating](https://www.electronics-tutorials.ws/resistor/res_7.html) - [8\. Resistors in AC Circuits](https://www.electronics-tutorials.ws/resistor/res_8.html) - [9\. Resistor Tutorial Summary](https://www.electronics-tutorials.ws/resistor/res_9.html) - [10\. Varistor Tutorial](https://www.electronics-tutorials.ws/resistor/varistor.html) - [11\. Resistor Colour Code Wheel](https://www.electronics-tutorials.ws/resistor/resistor-colour-code-wheel.html) - [12\. Potentiometers](https://www.electronics-tutorials.ws/resistor/potentiometer.html) - [13\. Resistivity](https://www.electronics-tutorials.ws/resistor/resistivity.html) - [14\. 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Readable Markdown	## Connecting Resistors Together in Series Individual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks. For resistors in series the equivalent resistance is the mathematical combination of the individual resistors connected together in the series string. A resistor is not only a fundamental electronic component that can be used to convert a voltage to a current or a current to a voltage, but by correctly adjusting its value a different weighting can be placed onto the converted current and/or the voltage allowing it to be used in voltage reference circuits and applications. Resistors in series or complicated resistor networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by [Ohm’s Law](https://www.electronics-tutorials.ws/dccircuits/dcp_2.html) and [Kirchhoff’s Circuit Laws](https://www.electronics-tutorials.ws/dccircuits/dcp_4.html). ## Resistors in Series Resistors are said to be connected in “Series”, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then we can see that resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path. Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example: ![series resistor current](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res43.gif) In the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them. ### Series Resistor Circuit ![resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res7.gif) As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is ![series resistance equation](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res44.gif) and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as: REQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ ![series resistors equivalent resistance](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res46.gif) So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ. Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value). This total resistance is generally known as the Equivalent Resistance and can be defined as; “a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as: ### Series Resistor Equation Rtotal = R1 + R2 + R3 + ….. Rn etc. Note then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances. \| \| \| \|---\|---\| \| ![equal resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res74.gif) \| If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc. \| \| \| \| \|---\|---\| \| ![unequal resistors in series](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res75.gif) \| If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc. \| One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ. ## Series Resistor Voltage The voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1, R2 and R3. VAB = VR1 + VR2 + VR3 = 9V. Using Ohm’s Law, the individual voltage drops across each resistor can be calculated as: The voltage drop across resistor, R1 is equal to: I\R1 = 1mA x 1kΩ = 1V The voltage drop across resistor, R2 is equal to: I\R2 = 1mA x 2kΩ = 2V The voltage drop across resistor, R3 is equal to: I\R3 = 1mA x 6kΩ = 6V Thus the voltage VAB being the sum of all the individual voltage drops in the resistors in series. That is: (1V + 2V + 6V) = 9V. This is also equal to the value of the supply voltage. Then the sum of the potential differences across all the resistors is equal in value to the total potential difference across the series combination. In this example it is 9V. The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as: ![series resistor voltages](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res45.gif) Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N* resistive components will have N-different voltages across it while maintaining a common current. By using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor. ## Resistors in Series Example No1 Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit. ![resistors in series circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res47.gif) All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form. \| \| \| \| \| \|---\|---\|---\|---\| \| Resistance \| Current \| Voltage \| Power \| \| R1 = 10Ω \| I1 = 200mA \| V1 = 2V \| P1 = 0.4W \| \| R2 = 20Ω \| I2 = 200mA \| V2 = 4V \| P2 = 0.8W \| \| R3 = 30Ω \| I3 = 200mA \| V3 = 6V \| P3 = 1.2W \| \| RT = 60Ω \| IT = 200mA \| VS = 12V \| PT = 2.4W \| Then for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W ## The Voltage Divider Circuit We can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a Voltage Divider Network. This simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it. The series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchhoff’s Voltage Law states that “the supply voltage in a closed circuit is equal to the sum of all the voltage drops (I\R) around the circuit” and this can be used to good effect. The Voltage Division Rule, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below. ### Voltage Divider Network ![voltage divider network](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res10.gif) The circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula. If more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance “R” (Ohms Law I\R*) values providing different but smaller voltage points from one single supply. So if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below. ![series divider circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/articles-divider8.gif) The potential divider circuit* above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows: ![voltage divider formula](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/articles-divider9.gif) We can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V). In this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) is equal to 100Ω or 100%, resistor R1 is 10% of RT. That is 10% of the source voltage VS will appear across it, 20% of VS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchhoff’s voltage law (KVL) around the closed loop path confirms this. Now lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage. Connecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below. ## Resistors in Series Example No2 Calculate the voltage drops across X and Y a) Without RL connected b) With RL connected ![potential divider network](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res15.gif) As you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, ([Resistors in Parallel](https://www.electronics-tutorials.ws/resistor/res_4.html)). Then we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio of Vout/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output. The effect of reducing a signal or voltage level is known as Attenuation so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction. A variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control. The Voltage Divider Circuit is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer. As well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchhoff’s or Thevenin’s theorems. ## Applications of Resistors in Series We have seen that Resistors in Series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If we replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured. For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures. ### Thermistor Circuit ![thermistor circuit](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res16.gif) At 25°C ![temperature at 25 degs](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res17.gif) At 100°C ![temperature at 100 degs](https://www.electronics-tutorials.ws/wp-content/uploads/2018/05/resistor-res18.gif) So by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range. ## Resistors in Series Summary To summarise the tutorial. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. Resistors in Series carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = I\*R ). Then series circuits are voltage dividers. In a series resistor network the individual resistors add together to give an equivalent resistance, ( RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit. In the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.
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