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Calculated Shard: 168 (from laksa153)

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curl -X POST \
  'http://laksa168.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.electronicshub.org/resistors-in-parallel/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.electronicshub.org/resistors-in-parallel/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.electronicshub.org\/resistors-in-parallel\/","crawl_time":1775822049,"first_indexed_time":1512452436,"http_code":200,"src_unparsed":"org,electronicshub!www,\/resistors-in-parallel\/ s443","src_root_hash":"7831353596008012568","history_drop_reason":null,"meta_title":"Resistors in Parallel | Equivalent Resistance Formula","meta_descriptions":["Get an idea about current calculation and applications of resistors in parallel connection. Here, the potential difference across each resistor is same."],"attrs_boilerpipe_text":"Two resistors are said to be connected in parallel if both the terminals of a resistor are connected to each respective terminal of other resistor. In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers.\nOutline\nResistors in Parallel\nEquivalent resistance Formula\nCurrent Calculation\nResistors in Parallel Example\nApplications\nResistors in Parallel\nIf two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential V\nAB\n.\nIf V\nAB\nis the potential supplied then\nV\nR1\n= V\nR2\n= V\nAB\nIn the following circuit, the resistors R1, R2 and R3 are connected in parallel combination.\nHere the supply potential is V\nAB\nbetween the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence V\nAB\n= V\nR1\n= V\nR2\n= V\nR3\n.\nWhere\nV\nR1\nis the potential across the resistor R1.\nV\nR2\nis the potential across the resistor R2.\nV\nR3\nis the potential across the resistor R3.\nBut the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel\nresistive circuits\n, the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.”\nHence\nI = I1 + I2 + I3.\nEquivalent resistance Formula\nAny number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors.\nIt has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit.\nHere, I = I1 + I2 + I3\nI1 = V \/ R1\nI2 = V \/ R2\nI3 = V \/ R3\nIf R\nT\nis the total resistance of the circuit then\nI = V \/ R\nT\nTherefore V \/ R\nT\n= V \/ R\n1\n+ V \/ R\n2\n+ V \/ R\n3\n1 \/ R\nT\n= 1 \/ R\n1\n+ 1 \/ R\n2\n+ 1 \/ R\n3\nIf R\neq\nis the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1\/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance R\neq\nis shown below for a parallel resistive circuit of n resistors.\n(1\/R\neq\n) = (1\/R1) + (1\/R2) + (1\/R3) + ……… + (1\/Rn)\nAn observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor.\nIf there are two resistors in parallel then the equivalent resistance is\n(1\/R\neq\n) = (1\/R1) + (1\/R2)\nR\nEQ\n= R\n1\n* R\n1\n\/ (R\n1\n+ R\n2\n)\nIf two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 2.\nSimilarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 3.\nThe parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω.\nEven though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form.\nAll the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too.\nCurrent Calculation\nCurrent in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law.\nConsider a parallel network of two resistors with supply voltage V between two points A and B.\nLet I be the total current in the following circuit.\nLet the current flowing through the resistor R\n1\nbe I\nR1\nand the current flowing through the resistor R\n2\nbe I\nR2\n.\nThen according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.”\nIf I\nT\nis the total current then\nI\nT\n= I\nR1\n+ I\nR2\nAs the voltage drop across each resistor is same\nI\nR1\n= V \/ R\n1\nAnd I\nR2\n= V \/ R\n2\nIf a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is\nI\nTotal\n= I\nR1\n+ I\nR2\n+…. + I\nRn\nIf the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits.\nIf a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance.\nResistors in Parallel Example\nConsider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel.\nThe resistance values of each resistor are\nR1 = 10 Ω\nR2 = 20 Ω\nR3 = 30 Ω\nR4 = 40 Ω\nThe supply voltage is V = 24V\nThe total current in the circuit can be calculated by two methods.\nFirst method is to calculate individual currents flowing through each resistor.\nIf I1 is the current flowing through the resistor R1, then according to Ohm’s law\nI1 = V \/ R\n1\n= 24\/10 = 2.4 A\nSimilarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law\nI2 = V \/ R\n2\n= 24\/20 = 1.2 A\nIf I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law\nI3 = V \/ R\n3\n= 24\/30 = 0.8 A\nAnd if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law\nI4 = V \/ R\n4\n= 24\/40 = 0.6 A\nIf I\nTOTAL\nis the total current in the circuit, then according to Kirchhoff’s Current law,\nI\nTOTAL\n= I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A\nThe second method to calculate current is by finding out the equivalent resistance of the circuit.\nThe equivalent resistance of the circuit is\n1\/R\nEQ\n= (1\/ R\n1\n) + (1\/R\n2\n) + (1\/ R\n3\n) + (1\/R\n4\n)\n1\/R\nEQ\n= (1\/10) + (1\/20) + (1\/30) + (1\/40)\nR\nEQ\n= 1\/2.083 = 4.8 Ω\nThis single resistor can be used to replace all the resistors in the parallel combination.\n∴ I\nTOTAL\n= V\/R\nEQ\n= 24\/4.8 = 5A.\nConsider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination.\nThe current flowing through R1 is I1 = 6A\nThe current flowing through R2 is I2 = 4A\nThe current flowing through R3 is I3 = 2A\nIn parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage.\nHere the supply voltage is V = 12 V.\nIf V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then\nV = V1 = V2 = V3 = 12V\nThen according to Ohm’s law\nR1 = V\n1\n\/ I\n1\nR1 = 12 \/ 6\nR1 = 2 Ω\nR2 = V\n2\n\/ I\n2\nR2 = 12 \/ 4\nR2 = 3 Ω\nR3 = V\n3\n\/ I\n3\nR3 = 12 \/ 2\nR3 = 6 Ω\nApplications\nThe concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like\nAnalog to Digital Converters\nand Digital to Analog Converters.\nRelated Posts:\nParallel Circuit | Basics, Equations, Voltage, Current\nSeries vs Parallel | A Comparison of Series and…\nResistors in Series and Parallel Combinations\nResistors In Series\nSeries Circuit | Basics, Characteristics,…\nPotential Difference In Resistor Networks","attrs_markdown":"[Skip to content](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#content)\n\n[![ElectronicsHub USA Logo](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2023\/04\/ElectronicsHub-Logo.jpg)](https:\/\/www.electronicshub.org\/)\n\n- [Guides & Howto](https:\/\/www.electronicshub.org\/how-to\/)\n- [Product Reviews](https:\/\/www.electronicshub.org\/reviews\/)\n- [Learn](https:\/\/www.electronicshub.org\/learn\/)\n- [Tutorials](https:\/\/www.electronicshub.org\/tutorials\/)\n- [About](https:\/\/www.electronicshub.org\/about\/)\n- [Contact](https:\/\/www.electronicshub.org\/contact\/)\n\n- [Guides & Howto](https:\/\/www.electronicshub.org\/how-to\/)\n- [Product Reviews](https:\/\/www.electronicshub.org\/reviews\/)\n- [Learn](https:\/\/www.electronicshub.org\/learn\/)\n- [Tutorials](https:\/\/www.electronicshub.org\/tutorials\/)\n- [About](https:\/\/www.electronicshub.org\/about\/)\n- [Contact](https:\/\/www.electronicshub.org\/contact\/)\n\n[![ElectronicsHub USA Logo](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2023\/04\/ElectronicsHub-Logo.jpg)](https:\/\/www.electronicshub.org\/)\n\n## [Home](https:\/\/www.electronicshub.org\/)\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2021\/04\/Arrow.png)\n\n- [Resistors](https:\/\/www.electronicshub.org\/resistors\/)\n\n# Resistors in Parallel\n- March 20, 2024\n- [By Ravi Teja](https:\/\/www.electronicshub.org\/author\/raviteja\/)\n\nTwo resistors are said to be connected in parallel if both the terminals of a resistor are connected to each respective terminal of other resistor. In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers.\n\nOutline\n\n[Toggle](https:\/\/www.electronicshub.org\/resistors-in-parallel\/)\n\n- [Resistors in Parallel](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Resistors_in_Parallel)\n  - [Equivalent resistance Formula](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Equivalent_resistance_Formula)\n  - [Current Calculation](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Current_Calculation)\n  - [Resistors in Parallel Example](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Resistors_in_Parallel_Example)\n  - [Applications](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Applications)\n## **Resistors in Parallel**\nIf two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential VAB.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Simple-Resistors-in-Parallel-Connection.png)\n\nIf VAB is the potential supplied then\n\nVR1 = VR2 = VAB\n\nIn the following circuit, the resistors R1, R2 and R3 are connected in parallel combination.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/3-Resistors-in-Parallel.png)\n\nHere the supply potential is VAB between the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence VAB = VR1 = VR2 = VR3.\n\nWhere\n\nVR1 is the potential across the resistor R1.\n\nVR2 is the potential across the resistor R2.\n\nVR3 is the potential across the resistor R3.\n\nBut the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel [resistive circuits](https:\/\/www.electronicshub.org\/ac-resistive-circuits\/), the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.”\n\nHence\n\nI = I1 + I2 + I3.\n\n### **Equivalent resistance Formula**\nAny number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors.\n\nIt has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Voltage-across-each-resistor-in-parallel.png)\n\nHere, I = I1 + I2 + I3\n\nI1 = V \/ R1\n\nI2 = V \/ R2\n\nI3 = V \/ R3\n\nIf RT is the total resistance of the circuit then\n\nI = V \/ RT\n\nTherefore V \/ RT = V \/ R1 + V \/ R2 + V \/ R3\n\n1 \/ RT = 1 \/ R1 + 1 \/ R2 + 1 \/ R3\n\nIf Req is the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1\/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance Req is shown below for a parallel resistive circuit of n resistors.\n\n(1\/Req) = (1\/R1) + (1\/R2) + (1\/R3) + ……… + (1\/Rn)\n\nAn observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor.\n\nIf there are two resistors in parallel then the equivalent resistance is\n\n(1\/Req) = (1\/R1) + (1\/R2)\n\nREQ = R1 \\* R1 \/ (R1 + R2)\n\nIf two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 2.\n\nSimilarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 3.\n\nThe parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω.\n\nEven though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Different-ways-of-connecting-resistors-in-parallel.jpg)\n\nAll the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too.\n\n### **Current Calculation**\nCurrent in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law.\n\nConsider a parallel network of two resistors with supply voltage V between two points A and B.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Simple-Resistors-in-Parallel-Connection.png)\n\nLet I be the total current in the following circuit.\n\nLet the current flowing through the resistor R1 be IR1 and the current flowing through the resistor R2 be IR2.\n\nThen according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.”\n\nIf IT is the total current then\n\nIT = IR1 + IR2\n\nAs the voltage drop across each resistor is same\n\nIR1 = V \/ R1\n\nAnd IR2 = V \/ R2\n\nIf a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is\n\nITotal = IR1 + IR2 +…. + IRn\n\nIf the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits.\n\nIf a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance.\n\n### **Resistors in Parallel Example**\n1. Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/4-Resistors-in-Parallel.png)\n\nThe resistance values of each resistor are\n\nR1 = 10 Ω\n\nR2 = 20 Ω\n\nR3 = 30 Ω\n\nR4 = 40 Ω\n\nThe supply voltage is V = 24V\n\nThe total current in the circuit can be calculated by two methods.\n\nFirst method is to calculate individual currents flowing through each resistor.\n\nIf I1 is the current flowing through the resistor R1, then according to Ohm’s law\n\nI1 = V \/ R1 = 24\/10 = 2.4 A\n\nSimilarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law\n\nI2 = V \/ R2 = 24\/20 = 1.2 A\n\nIf I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law\n\nI3 = V \/ R3 = 24\/30 = 0.8 A\n\nAnd if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law\n\nI4 = V \/ R4 = 24\/40 = 0.6 A\n\nIf ITOTAL is the total current in the circuit, then according to Kirchhoff’s Current law,\n\nITOTAL = I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A\n\nThe second method to calculate current is by finding out the equivalent resistance of the circuit.\n\nThe equivalent resistance of the circuit is\n\n1\/REQ = (1\/ R1) + (1\/R2) + (1\/ R3) + (1\/R4)\n\n1\/REQ = (1\/10) + (1\/20) + (1\/30) + (1\/40)\n\nREQ = 1\/2.083 = 4.8 Ω\n\nThis single resistor can be used to replace all the resistors in the parallel combination.\n\n∴ ITOTAL = V\/REQ = 24\/4.8 = 5A.\n\nConsider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination.\n\n[![Untitled](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Untitled.jpg)](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Untitled.jpg)\n\nThe current flowing through R1 is I1 = 6A\n\nThe current flowing through R2 is I2 = 4A\n\nThe current flowing through R3 is I3 = 2A\n\nIn parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage.\n\nHere the supply voltage is V = 12 V.\n\nIf V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then\n\nV = V1 = V2 = V3 = 12V\n\nThen according to Ohm’s law\n\nR1 = V1 \/ I1\n\nR1 = 12 \/ 6\n\nR1 = 2 Ω\n\nR2 = V2 \/ I2\n\nR2 = 12 \/ 4\n\nR2 = 3 Ω\n\nR3 = V3 \/ I3\n\nR3 = 12 \/ 2\n\nR3 = 6 Ω\n\n### **Applications**\nThe concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like [Analog to Digital Converters](https:\/\/www.electronicshub.org\/analog-circuits-and-digital-circuits\/) and Digital to Analog Converters.\n\n### Related Posts:\n- [Parallel Circuit \\| Basics, Equations, Voltage, Current](https:\/\/www.electronicshub.org\/parallel-circuit\/)\n- [Series vs Parallel \\| A Comparison of Series and…](https:\/\/www.electronicshub.org\/series-vs-parallel\/)\n- [Resistors in Series and Parallel Combinations](https:\/\/www.electronicshub.org\/resistors-in-series-and-parallel-combinations\/)\n- [Resistors In Series](https:\/\/www.electronicshub.org\/resistors-in-series\/)\n- [Series Circuit \\| Basics, Characteristics,…](https:\/\/www.electronicshub.org\/series-circuit\/)\n- [Potential Difference In Resistor Networks](https:\/\/www.electronicshub.org\/potential-difference-in-resistor-networks\/)\n\n## 2 Responses\n1. ![](https:\/\/secure.gravatar.com\/avatar\/b9e647df801c672c0a4a5052909c423fa9db62b9a22fefa998423d9d44e87571?s=42&d=blank&r=g) **Anup Sonkusare** says:\n   \n   [March 9, 2018 at 10:25 am](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#comment-310659)\n   \n   Really impressed the way you guys explained each and every topic very very clearly..Thank a Lot\n   \n   [Reply](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#comment-310659)\n2. ![](https:\/\/secure.gravatar.com\/avatar\/10fe0ab7e61815a29ac251c3c652641dbe637df8852f23e95f7f70907174670d?s=42&d=blank&r=g) **Narmadha Sowndar** says:\n   \n   [July 25, 2018 at 12:30 pm](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#comment-315931)\n   \n   Nice…. good job\n   \n   [Reply](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#comment-315931)\n## Leave a Reply [Cancel reply](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#respond)\n\n## Get our Latest Newletters\nGet great content that you love. 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In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers.\n\nOutline\n\n- [Resistors in Parallel](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Resistors_in_Parallel)\n  - [Equivalent resistance Formula](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Equivalent_resistance_Formula)\n  - [Current Calculation](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Current_Calculation)\n  - [Resistors in Parallel Example](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Resistors_in_Parallel_Example)\n  - [Applications](https:\/\/www.electronicshub.org\/resistors-in-parallel\/#Applications)\n## **Resistors in Parallel**\nIf two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential VAB.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Simple-Resistors-in-Parallel-Connection.png)\n\nIf VAB is the potential supplied then\n\nVR1 = VR2 = VAB\n\nIn the following circuit, the resistors R1, R2 and R3 are connected in parallel combination.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/3-Resistors-in-Parallel.png)\n\nHere the supply potential is VAB between the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence VAB = VR1 = VR2 = VR3.\n\nWhere\n\nVR1 is the potential across the resistor R1.\n\nVR2 is the potential across the resistor R2.\n\nVR3 is the potential across the resistor R3.\n\nBut the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel [resistive circuits](https:\/\/www.electronicshub.org\/ac-resistive-circuits\/), the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.”\n\nHence\n\nI = I1 + I2 + I3.\n\n### **Equivalent resistance Formula**\nAny number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors.\n\nIt has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Voltage-across-each-resistor-in-parallel.png)\n\nHere, I = I1 + I2 + I3\n\nI1 = V \/ R1\n\nI2 = V \/ R2\n\nI3 = V \/ R3\n\nIf RT is the total resistance of the circuit then\n\nI = V \/ RT\n\nTherefore V \/ RT = V \/ R1 + V \/ R2 + V \/ R3\n\n1 \/ RT = 1 \/ R1 + 1 \/ R2 + 1 \/ R3\n\nIf Req is the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1\/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance Req is shown below for a parallel resistive circuit of n resistors.\n\n(1\/Req) = (1\/R1) + (1\/R2) + (1\/R3) + ……… + (1\/Rn)\n\nAn observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor.\n\nIf there are two resistors in parallel then the equivalent resistance is\n\n(1\/Req) = (1\/R1) + (1\/R2)\n\nREQ = R1 \\* R1 \/ (R1 + R2)\n\nIf two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 2.\n\nSimilarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R \/ 3.\n\nThe parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω.\n\nEven though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Different-ways-of-connecting-resistors-in-parallel.jpg)\n\nAll the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too.\n\n### **Current Calculation**\nCurrent in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law.\n\nConsider a parallel network of two resistors with supply voltage V between two points A and B.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Simple-Resistors-in-Parallel-Connection.png)\n\nLet I be the total current in the following circuit.\n\nLet the current flowing through the resistor R1 be IR1 and the current flowing through the resistor R2 be IR2.\n\nThen according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.”\n\nIf IT is the total current then\n\nIT = IR1 + IR2\n\nAs the voltage drop across each resistor is same\n\nIR1 = V \/ R1\n\nAnd IR2 = V \/ R2\n\nIf a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is\n\nITotal = IR1 + IR2 +…. + IRn\n\nIf the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits.\n\nIf a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance.\n\n### **Resistors in Parallel Example**\n1. Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel.\n\n![](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/4-Resistors-in-Parallel.png)\n\nThe resistance values of each resistor are\n\nR1 = 10 Ω\n\nR2 = 20 Ω\n\nR3 = 30 Ω\n\nR4 = 40 Ω\n\nThe supply voltage is V = 24V\n\nThe total current in the circuit can be calculated by two methods.\n\nFirst method is to calculate individual currents flowing through each resistor.\n\nIf I1 is the current flowing through the resistor R1, then according to Ohm’s law\n\nI1 = V \/ R1 = 24\/10 = 2.4 A\n\nSimilarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law\n\nI2 = V \/ R2 = 24\/20 = 1.2 A\n\nIf I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law\n\nI3 = V \/ R3 = 24\/30 = 0.8 A\n\nAnd if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law\n\nI4 = V \/ R4 = 24\/40 = 0.6 A\n\nIf ITOTAL is the total current in the circuit, then according to Kirchhoff’s Current law,\n\nITOTAL = I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A\n\nThe second method to calculate current is by finding out the equivalent resistance of the circuit.\n\nThe equivalent resistance of the circuit is\n\n1\/REQ = (1\/ R1) + (1\/R2) + (1\/ R3) + (1\/R4)\n\n1\/REQ = (1\/10) + (1\/20) + (1\/30) + (1\/40)\n\nREQ = 1\/2.083 = 4.8 Ω\n\nThis single resistor can be used to replace all the resistors in the parallel combination.\n\n∴ ITOTAL = V\/REQ = 24\/4.8 = 5A.\n\nConsider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination.\n\n[![Untitled](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Untitled.jpg)](https:\/\/www.electronicshub.org\/wp-content\/uploads\/2014\/12\/Untitled.jpg)\n\nThe current flowing through R1 is I1 = 6A\n\nThe current flowing through R2 is I2 = 4A\n\nThe current flowing through R3 is I3 = 2A\n\nIn parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage.\n\nHere the supply voltage is V = 12 V.\n\nIf V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then\n\nV = V1 = V2 = V3 = 12V\n\nThen according to Ohm’s law\n\nR1 = V1 \/ I1\n\nR1 = 12 \/ 6\n\nR1 = 2 Ω\n\nR2 = V2 \/ I2\n\nR2 = 12 \/ 4\n\nR2 = 3 Ω\n\nR3 = V3 \/ I3\n\nR3 = 12 \/ 2\n\nR3 = 6 Ω\n\n### **Applications**\nThe concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like [Analog to Digital Converters](https:\/\/www.electronicshub.org\/analog-circuits-and-digital-circuits\/) and Digital to Analog Converters.\n\n### Related Posts:\n- [Parallel Circuit \\| Basics, Equations, Voltage, Current](https:\/\/www.electronicshub.org\/parallel-circuit\/)\n- [Series vs Parallel \\| A Comparison of Series and…](https:\/\/www.electronicshub.org\/series-vs-parallel\/)\n- [Resistors in Series and Parallel Combinations](https:\/\/www.electronicshub.org\/resistors-in-series-and-parallel-combinations\/)\n- [Resistors In Series](https:\/\/www.electronicshub.org\/resistors-in-series\/)\n- [Series Circuit \\| Basics, Characteristics,…](https:\/\/www.electronicshub.org\/series-circuit\/)\n- [Potential Difference In Resistor Networks](https:\/\/www.electronicshub.org\/potential-difference-in-resistor-networks\/)","meta_canonical":null}

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Boilerpipe Text	Two resistors are said to be connected in parallel if both the terminals of a resistor are connected to each respective terminal of other resistor. In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers. Outline Resistors in Parallel Equivalent resistance Formula Current Calculation Resistors in Parallel Example Applications Resistors in Parallel If two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential V AB . If V AB is the potential supplied then V R1 = V R2 = V AB In the following circuit, the resistors R1, R2 and R3 are connected in parallel combination. Here the supply potential is V AB between the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence V AB = V R1 = V R2 = V R3 . Where V R1 is the potential across the resistor R1. V R2 is the potential across the resistor R2. V R3 is the potential across the resistor R3. But the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel resistive circuits , the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.” Hence I = I1 + I2 + I3. Equivalent resistance Formula Any number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors. It has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit. Here, I = I1 + I2 + I3 I1 = V / R1 I2 = V / R2 I3 = V / R3 If R T is the total resistance of the circuit then I = V / R T Therefore V / R T = V / R 1 + V / R 2 + V / R 3 1 / R T = 1 / R 1 + 1 / R 2 + 1 / R 3 If R eq is the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance R eq is shown below for a parallel resistive circuit of n resistors. (1/R eq ) = (1/R1) + (1/R2) + (1/R3) + ……… + (1/Rn) An observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor. If there are two resistors in parallel then the equivalent resistance is (1/R eq ) = (1/R1) + (1/R2) R EQ = R 1 * R 1 / (R 1 + R 2 ) If two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 2. Similarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 3. The parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω. Even though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form. All the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too. Current Calculation Current in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law. Consider a parallel network of two resistors with supply voltage V between two points A and B. Let I be the total current in the following circuit. Let the current flowing through the resistor R 1 be I R1 and the current flowing through the resistor R 2 be I R2 . Then according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.” If I T is the total current then I T = I R1 + I R2 As the voltage drop across each resistor is same I R1 = V / R 1 And I R2 = V / R 2 If a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is I Total = I R1 + I R2 +…. + I Rn If the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits. If a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance. Resistors in Parallel Example Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel. The resistance values of each resistor are R1 = 10 Ω R2 = 20 Ω R3 = 30 Ω R4 = 40 Ω The supply voltage is V = 24V The total current in the circuit can be calculated by two methods. First method is to calculate individual currents flowing through each resistor. If I1 is the current flowing through the resistor R1, then according to Ohm’s law I1 = V / R 1 = 24/10 = 2.4 A Similarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law I2 = V / R 2 = 24/20 = 1.2 A If I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law I3 = V / R 3 = 24/30 = 0.8 A And if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law I4 = V / R 4 = 24/40 = 0.6 A If I TOTAL is the total current in the circuit, then according to Kirchhoff’s Current law, I TOTAL = I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A The second method to calculate current is by finding out the equivalent resistance of the circuit. The equivalent resistance of the circuit is 1/R EQ = (1/ R 1 ) + (1/R 2 ) + (1/ R 3 ) + (1/R 4 ) 1/R EQ = (1/10) + (1/20) + (1/30) + (1/40) R EQ = 1/2.083 = 4.8 Ω This single resistor can be used to replace all the resistors in the parallel combination. ∴ I TOTAL = V/R EQ = 24/4.8 = 5A. Consider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination. The current flowing through R1 is I1 = 6A The current flowing through R2 is I2 = 4A The current flowing through R3 is I3 = 2A In parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage. Here the supply voltage is V = 12 V. If V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then V = V1 = V2 = V3 = 12V Then according to Ohm’s law R1 = V 1 / I 1 R1 = 12 / 6 R1 = 2 Ω R2 = V 2 / I 2 R2 = 12 / 4 R2 = 3 Ω R3 = V 3 / I 3 R3 = 12 / 2 R3 = 6 Ω Applications The concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like Analog to Digital Converters and Digital to Analog Converters. Related Posts: Parallel Circuit \| Basics, Equations, Voltage, Current Series vs Parallel \| A Comparison of Series and… Resistors in Series and Parallel Combinations Resistors In Series Series Circuit \| Basics, Characteristics,… Potential Difference In Resistor Networks
Markdown	[Skip to content](https://www.electronicshub.org/resistors-in-parallel/#content) [![ElectronicsHub USA Logo](https://www.electronicshub.org/wp-content/uploads/2023/04/ElectronicsHub-Logo.jpg)](https://www.electronicshub.org/) - [Guides & Howto](https://www.electronicshub.org/how-to/) - [Product Reviews](https://www.electronicshub.org/reviews/) - [Learn](https://www.electronicshub.org/learn/) - [Tutorials](https://www.electronicshub.org/tutorials/) - [About](https://www.electronicshub.org/about/) - [Contact](https://www.electronicshub.org/contact/) - [Guides & Howto](https://www.electronicshub.org/how-to/) - [Product Reviews](https://www.electronicshub.org/reviews/) - [Learn](https://www.electronicshub.org/learn/) - [Tutorials](https://www.electronicshub.org/tutorials/) - [About](https://www.electronicshub.org/about/) - [Contact](https://www.electronicshub.org/contact/) [![ElectronicsHub USA Logo](https://www.electronicshub.org/wp-content/uploads/2023/04/ElectronicsHub-Logo.jpg)](https://www.electronicshub.org/) ## [Home](https://www.electronicshub.org/) ![](https://www.electronicshub.org/wp-content/uploads/2021/04/Arrow.png) - [Resistors](https://www.electronicshub.org/resistors/) # Resistors in Parallel - March 20, 2024 - [By Ravi Teja](https://www.electronicshub.org/author/raviteja/) Two resistors are said to be connected in parallel if both the terminals of a resistor are connected to each respective terminal of other resistor. In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers. Outline [Toggle](https://www.electronicshub.org/resistors-in-parallel/) - [Resistors in Parallel](https://www.electronicshub.org/resistors-in-parallel/#Resistors_in_Parallel) - [Equivalent resistance Formula](https://www.electronicshub.org/resistors-in-parallel/#Equivalent_resistance_Formula) - [Current Calculation](https://www.electronicshub.org/resistors-in-parallel/#Current_Calculation) - [Resistors in Parallel Example](https://www.electronicshub.org/resistors-in-parallel/#Resistors_in_Parallel_Example) - [Applications](https://www.electronicshub.org/resistors-in-parallel/#Applications) ## Resistors in Parallel If two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential VAB. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Simple-Resistors-in-Parallel-Connection.png) If VAB is the potential supplied then VR1 = VR2 = VAB In the following circuit, the resistors R1, R2 and R3 are connected in parallel combination. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/3-Resistors-in-Parallel.png) Here the supply potential is VAB between the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence VAB = VR1 = VR2 = VR3. Where VR1 is the potential across the resistor R1. VR2 is the potential across the resistor R2. VR3 is the potential across the resistor R3. But the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel [resistive circuits](https://www.electronicshub.org/ac-resistive-circuits/), the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.” Hence I = I1 + I2 + I3. ### Equivalent resistance Formula Any number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors. It has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Voltage-across-each-resistor-in-parallel.png) Here, I = I1 + I2 + I3 I1 = V / R1 I2 = V / R2 I3 = V / R3 If RT is the total resistance of the circuit then I = V / RT Therefore V / RT = V / R1 + V / R2 + V / R3 1 / RT = 1 / R1 + 1 / R2 + 1 / R3 If Req is the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance Req is shown below for a parallel resistive circuit of n resistors. (1/Req) = (1/R1) + (1/R2) + (1/R3) + ……… + (1/Rn) An observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor. If there are two resistors in parallel then the equivalent resistance is (1/Req) = (1/R1) + (1/R2) REQ = R1 \* R1 / (R1 + R2) If two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 2. Similarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 3. The parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω. Even though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Different-ways-of-connecting-resistors-in-parallel.jpg) All the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too. ### Current Calculation Current in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law. Consider a parallel network of two resistors with supply voltage V between two points A and B. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Simple-Resistors-in-Parallel-Connection.png) Let I be the total current in the following circuit. Let the current flowing through the resistor R1 be IR1 and the current flowing through the resistor R2 be IR2. Then according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.” If IT is the total current then IT = IR1 + IR2 As the voltage drop across each resistor is same IR1 = V / R1 And IR2 = V / R2 If a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is ITotal = IR1 + IR2 +…. + IRn If the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits. If a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance. ### Resistors in Parallel Example 1. Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/4-Resistors-in-Parallel.png) The resistance values of each resistor are R1 = 10 Ω R2 = 20 Ω R3 = 30 Ω R4 = 40 Ω The supply voltage is V = 24V The total current in the circuit can be calculated by two methods. First method is to calculate individual currents flowing through each resistor. If I1 is the current flowing through the resistor R1, then according to Ohm’s law I1 = V / R1 = 24/10 = 2.4 A Similarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law I2 = V / R2 = 24/20 = 1.2 A If I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law I3 = V / R3 = 24/30 = 0.8 A And if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law I4 = V / R4 = 24/40 = 0.6 A If ITOTAL is the total current in the circuit, then according to Kirchhoff’s Current law, ITOTAL = I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A The second method to calculate current is by finding out the equivalent resistance of the circuit. The equivalent resistance of the circuit is 1/REQ = (1/ R1) + (1/R2) + (1/ R3) + (1/R4) 1/REQ = (1/10) + (1/20) + (1/30) + (1/40) REQ = 1/2.083 = 4.8 Ω This single resistor can be used to replace all the resistors in the parallel combination. ∴ ITOTAL = V/REQ = 24/4.8 = 5A. Consider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination. [![Untitled](https://www.electronicshub.org/wp-content/uploads/2014/12/Untitled.jpg)](https://www.electronicshub.org/wp-content/uploads/2014/12/Untitled.jpg) The current flowing through R1 is I1 = 6A The current flowing through R2 is I2 = 4A The current flowing through R3 is I3 = 2A In parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage. Here the supply voltage is V = 12 V. If V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then V = V1 = V2 = V3 = 12V Then according to Ohm’s law R1 = V1 / I1 R1 = 12 / 6 R1 = 2 Ω R2 = V2 / I2 R2 = 12 / 4 R2 = 3 Ω R3 = V3 / I3 R3 = 12 / 2 R3 = 6 Ω ### Applications The concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like [Analog to Digital Converters](https://www.electronicshub.org/analog-circuits-and-digital-circuits/) and Digital to Analog Converters. ### Related Posts: - [Parallel Circuit \\| Basics, Equations, Voltage, Current](https://www.electronicshub.org/parallel-circuit/) - [Series vs Parallel \\| A Comparison of Series and…](https://www.electronicshub.org/series-vs-parallel/) - [Resistors in Series and Parallel Combinations](https://www.electronicshub.org/resistors-in-series-and-parallel-combinations/) - [Resistors In Series](https://www.electronicshub.org/resistors-in-series/) - [Series Circuit \\| Basics, Characteristics,…](https://www.electronicshub.org/series-circuit/) - [Potential Difference In Resistor Networks](https://www.electronicshub.org/potential-difference-in-resistor-networks/) ## 2 Responses 1. ![](https://secure.gravatar.com/avatar/b9e647df801c672c0a4a5052909c423fa9db62b9a22fefa998423d9d44e87571?s=42&d=blank&r=g) Anup Sonkusare says: [March 9, 2018 at 10:25 am](https://www.electronicshub.org/resistors-in-parallel/#comment-310659) Really impressed the way you guys explained each and every topic very very clearly..Thank a Lot [Reply](https://www.electronicshub.org/resistors-in-parallel/#comment-310659) 2. ![](https://secure.gravatar.com/avatar/10fe0ab7e61815a29ac251c3c652641dbe637df8852f23e95f7f70907174670d?s=42&d=blank&r=g) Narmadha Sowndar says: [July 25, 2018 at 12:30 pm](https://www.electronicshub.org/resistors-in-parallel/#comment-315931) Nice…. good job [Reply](https://www.electronicshub.org/resistors-in-parallel/#comment-315931) ## Leave a Reply [Cancel reply](https://www.electronicshub.org/resistors-in-parallel/#respond) ## Get our Latest Newletters Get great content that you love. 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Readable Markdown	Two resistors are said to be connected in parallel if both the terminals of a resistor are connected to each respective terminal of other resistor. In a network of parallel resistors, current can take more than one path unlike in series resistor network as there are multiple paths for the current to flow. Hence parallel resistor circuits are current dividers. Outline - [Resistors in Parallel](https://www.electronicshub.org/resistors-in-parallel/#Resistors_in_Parallel) - [Equivalent resistance Formula](https://www.electronicshub.org/resistors-in-parallel/#Equivalent_resistance_Formula) - [Current Calculation](https://www.electronicshub.org/resistors-in-parallel/#Current_Calculation) - [Resistors in Parallel Example](https://www.electronicshub.org/resistors-in-parallel/#Resistors_in_Parallel_Example) - [Applications](https://www.electronicshub.org/resistors-in-parallel/#Applications) ## Resistors in Parallel If two or more resistors are connected in parallel, then the potential difference across each resistor is same. Resistors in parallel connection are connected to the same nodes. This can be identified by the presence of more than one path for the current to flow. For example, the circuit shown below is a parallel connection of resistors. The potential difference across the resistor R1 is same as that across the resistor R2 which is equal to the supply potential VAB. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Simple-Resistors-in-Parallel-Connection.png) If VAB is the potential supplied then VR1 = VR2 = VAB In the following circuit, the resistors R1, R2 and R3 are connected in parallel combination. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/3-Resistors-in-Parallel.png) Here the supply potential is VAB between the points A and B. Since the resistors R1, R2 and R3 are connected in parallel combination the potential difference across each resistor is same as the supply. Hence VAB = VR1 = VR2 = VR3. Where VR1 is the potential across the resistor R1. VR2 is the potential across the resistor R2. VR3 is the potential across the resistor R3. But the current flowing through these three resistors is different. If I is the current leaving the node A then it has three paths to reach the node B. The current flowing through each resistor is dependent on its resistance. Hence in case of parallel [resistive circuits](https://www.electronicshub.org/ac-resistive-circuits/), the current is not same in all the resistors. If I1 is the current flowing through the resistor R1, I2 is the current flowing through the resistor R2 and I3 is the current flowing through the resistor R3 then the currents I, I1, I2 and I3 can be related with the help of Kirchhoff’s Current Law. According to Kirchhoff’s Current Law, “the sum of currents entering a node is equal to the sum of currents leaving the node.” Hence I = I1 + I2 + I3. ### Equivalent resistance Formula Any number of resistors connected in a parallel combination can be replaced by a single resistor with the resistance equal to the equivalent resistance of the parallel combination resistors. It has been established that the voltage across each resistor in a parallel combination is same and the total current is equal to sum of individual currents. Consider the following circuit. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Voltage-across-each-resistor-in-parallel.png) Here, I = I1 + I2 + I3 I1 = V / R1 I2 = V / R2 I3 = V / R3 If RT is the total resistance of the circuit then I = V / RT Therefore V / RT = V / R1 + V / R2 + V / R3 1 / RT = 1 / R1 + 1 / R2 + 1 / R3 If Req is the equivalent resistance of the circuit then it is calculated from adding the reciprocal values of individual resistances (1/R). The inverse of this algebraic sum will give the equivalent resistance. The equation for equivalent resistance Req is shown below for a parallel resistive circuit of n resistors. (1/Req) = (1/R1) + (1/R2) + (1/R3) + ……… + (1/Rn) An observation can be made from the above equation that the equivalent resistance of resistors connected in parallel is always smaller than the resistance of smallest resistor. If there are two resistors in parallel then the equivalent resistance is (1/Req) = (1/R1) + (1/R2) REQ = R1 \* R1 / (R1 + R2) If two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 2. Similarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 3. The parallel connection of resistors gives the value of Conductance. Conductance is the reciprocal of resistance. It is generally represented by the symbol G. The units of Conductance are Siemens represented by the symbol S. Previously the units of conductance are Mho (℧) which is backward spelling of Ohm and the symbol is upside down representation of Ω. Even though the parallel resistors are connected between two nodes, the representation of this connection can take any of the following form. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Different-ways-of-connecting-resistors-in-parallel.jpg) All the above mentioned combinations are parallel resistive circuits and all the rules of parallel resistorsare applicable to above mentioned combinations too. ### Current Calculation Current in each branch of a parallel resistive circuit is different from the other. Since the voltage across each resistor is same, the current flowing through each resistor is dependent on the resistance of that resistor. Hence if the resistance value in a branch is different from the other branch then the current in those branches will be different. The value of that current can be determined by using Ohm’s Law. Consider a parallel network of two resistors with supply voltage V between two points A and B. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/Simple-Resistors-in-Parallel-Connection.png) Let I be the total current in the following circuit. Let the current flowing through the resistor R1 be IR1 and the current flowing through the resistor R2 be IR2. Then according to Kirchhoff’s Current Law, “the total current entering a circuit is equal to that leaving the circuit.” If IT is the total current then IT = IR1 + IR2 As the voltage drop across each resistor is same IR1 = V / R1 And IR2 = V / R2 If a parallel resistive circuit consisting of n resistors is considered, then the total current in the circuit is ITotal = IR1 + IR2 +…. + IRn If the series resistive circuits are called Voltage Divider Circuits then similarly the parallel resistive circuits are called Current Divider Circuits. If a parallel resistive circuit of n resistors with different resistances is considered then it is possible to have n different paths for the current to flow and n different values of current through that paths. The resistors in a parallel combination can be interchanged without affecting the total current and equivalent resistance. ### Resistors in Parallel Example 1. Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel. ![](https://www.electronicshub.org/wp-content/uploads/2014/12/4-Resistors-in-Parallel.png) The resistance values of each resistor are R1 = 10 Ω R2 = 20 Ω R3 = 30 Ω R4 = 40 Ω The supply voltage is V = 24V The total current in the circuit can be calculated by two methods. First method is to calculate individual currents flowing through each resistor. If I1 is the current flowing through the resistor R1, then according to Ohm’s law I1 = V / R1 = 24/10 = 2.4 A Similarly if I2 is the current flowing through the resistor R2, thenaccording to Ohm’s law I2 = V / R2 = 24/20 = 1.2 A If I3 is the current flowing through the resistor R3, thenaccording to Ohm’s law I3 = V / R3 = 24/30 = 0.8 A And if I4 is the current flowing through the resistor R4, thenaccording to Ohm’s law I4 = V / R4 = 24/40 = 0.6 A If ITOTAL is the total current in the circuit, then according to Kirchhoff’s Current law, ITOTAL = I1 + I2 + I3 + I4 = 2.4 + 1.2 + 0.8 + 0.6 = 5A The second method to calculate current is by finding out the equivalent resistance of the circuit. The equivalent resistance of the circuit is 1/REQ = (1/ R1) + (1/R2) + (1/ R3) + (1/R4) 1/REQ = (1/10) + (1/20) + (1/30) + (1/40) REQ = 1/2.083 = 4.8 Ω This single resistor can be used to replace all the resistors in the parallel combination. ∴ ITOTAL = V/REQ = 24/4.8 = 5A. Consider the following circuit where three resistors R1, R2 and R3 are connected in a parallel combination. [![Untitled](https://www.electronicshub.org/wp-content/uploads/2014/12/Untitled.jpg)](https://www.electronicshub.org/wp-content/uploads/2014/12/Untitled.jpg) The current flowing through R1 is I1 = 6A The current flowing through R2 is I2 = 4A The current flowing through R3 is I3 = 2A In parallel resistive circuits, the voltage across each resistor is same and is equal to the supply voltage. Here the supply voltage is V = 12 V. If V1 is the voltage across the resistor R1, V2 is the voltage across the resistor R2 and V3 is the voltage across the resistor R3 then V = V1 = V2 = V3 = 12V Then according to Ohm’s law R1 = V1 / I1 R1 = 12 / 6 R1 = 2 Ω R2 = V2 / I2 R2 = 12 / 4 R2 = 3 Ω R3 = V3 / I3 R3 = 12 / 2 R3 = 6 Ω ### Applications The concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like [Analog to Digital Converters](https://www.electronicshub.org/analog-circuits-and-digital-circuits/) and Digital to Analog Converters. ### Related Posts: - [Parallel Circuit \\| Basics, Equations, Voltage, Current](https://www.electronicshub.org/parallel-circuit/) - [Series vs Parallel \\| A Comparison of Series and…](https://www.electronicshub.org/series-vs-parallel/) - [Resistors in Series and Parallel Combinations](https://www.electronicshub.org/resistors-in-series-and-parallel-combinations/) - [Resistors In Series](https://www.electronicshub.org/resistors-in-series/) - [Series Circuit \\| Basics, Characteristics,…](https://www.electronicshub.org/series-circuit/) - [Potential Difference In Resistor Networks](https://www.electronicshub.org/potential-difference-in-resistor-networks/)
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