{"id":628253,"date":"2023-06-23T16:24:49","date_gmt":"2023-06-23T10:54:49","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=628253"},"modified":"2025-04-28T15:35:41","modified_gmt":"2025-04-28T10:05:41","slug":"equivalent-resistance-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/equivalent-resistance-formula\/","title":{"rendered":"Equivalent Resistance Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/equivalent-resistance-formula\/#Introduction\" title=\"Introduction: \">Introduction: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/equivalent-resistance-formula\/#Equivalent_Resistance_Formula_for_Resistors_in_series\" title=\"Equivalent Resistance Formula for Resistors in series:\">Equivalent Resistance Formula for Resistors in series:<\/a><\/li><\/ul><\/nav><\/div>\n<h3><b><span data-contrast=\"none\">Introduction:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h3>\n<p><span data-contrast=\"none\">Equivalent resistance formulas are used in <strong>electrical circuits<\/strong> to simplify complex circuits into a single equivalent resistance. The equivalent resistance represents the total resistance that a current would encounter if it flowed through the entire circuit. Here are some important formulas related to equivalent resistance:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Equivalent_Resistance_Formula_for_Resistors_in_series\"><\/span><b><span data-contrast=\"none\">Equivalent Resistance Formula for Resistors in series:<\/span><\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span data-contrast=\"none\">Consider a simple circuit with three resistors R1, R2, and R3 connected in series along with an <strong>Ammeter<\/strong> and a plug key.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:3111,&quot;335559737&quot;:3121,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628254 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-161933.png\" alt=\"\" width=\"255\" height=\"175\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span data-contrast=\"none\">Resistors in series<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:196}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Close the plug key and note down the Ammeter reading. Next, place the ammeter between the resistors R1 and R2, and then between R2 and R3 and note down the respective ammeter readings.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:196}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">From the readings recorded, we see that the current is the same in each reading. Let this current be \u2018I\u2019 ampere. So, in a series of combinations of resistors, the current flowing is the same throughout the circuit.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Now remove the ammeter and insert a voltmeter across the start of the first resistor and the end of the third resistor. Then plug the key and note the potential difference across the resistors. Let\u2019s say it\u2019s \u2018V\u2019 volts.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:273}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628255 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-161953.png\" alt=\"\" width=\"276\" height=\"186\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Disconnect the voltmeter and insert three voltmeters in the circuit, one across each of the resistors. Then plug the key and measure the potential difference across each of the resistors. You will notice that the potential difference across each of the resistors is different. Let\u2019s call them V1, V2, and V3 respectively.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:3118,&quot;335559737&quot;:3114,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628256 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-162022.png\" alt=\"\" width=\"258\" height=\"182\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Even though the voltages are different, you will notice that the potential difference V is equal to the sum of the potential differences V1, V2, and V3.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:282}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V = V1 + V2 + V3<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(1)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:262,&quot;469777462&quot;:[2191,3170],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Let the 3 resistors together form resistance of R ohms. Thus by Ohm\u2019s Law,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559737&quot;:4032,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:284}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V = IR<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(2)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:262,&quot;469777462&quot;:[1471,2450],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Similarly, applying Ohm\u2019s law for each resistor,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:267}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V1 = IR1<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(3)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:262,&quot;469777462&quot;:[2191,3170],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V2 = IR2<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(4)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:262,&quot;469777462&quot;:[1471,2450],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V3 = IR3<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(5)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:262,&quot;469777462&quot;:[1471,2450],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Now on substituting equations (2), (3), (4), and (5) in equation (1), IR = IR1 + IR2 + IR3<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559737&quot;:2736,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:414}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 R<\/span><span data-contrast=\"none\">s<\/span><span data-contrast=\"none\"> = R1 + R2 + R3<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:272}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Thus, when two or more resistors are connected in series, then the overall combined resistance, denoted by \u2018Rs\u2019, is the sum of the individual resistances.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:289}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Equivalent Resistance Formula for Resistors in Parallel:<\/span><\/b><br \/>\n<span data-contrast=\"none\">Consider a simple circuit with three resistors R1, R2 and R3, an Ammeter and a plug key. In this circuit, we have 3 resistors of different values connected in parallel since all the resistors have common start and endpoints. Let the points be X and Y.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:3125,&quot;335559737&quot;:3125,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628257 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-162040.png\" alt=\"\" width=\"256\" height=\"197\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span data-contrast=\"none\">Resistors in parallel<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The potential difference is always measured between two points. If the two points are common, it means the potential difference across each of the resistors will be the same.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:271}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The points X and Y are common for each of the resistors and also for the battery. So, if the potential difference across the battery is \u2018V\u2019 volts, then the potential difference across each resistor will also be V volts.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559737&quot;:504,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:273}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">In this circuit, the current across each resistor will not be the same.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Let the current across R1, R2, and R3 be I1, I2, and I3 respectively. Let the total current flowing in the circuit be I. Then the total current I will be equal to the sum of the separate currents flowing through each of the resistors.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559737&quot;:144,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:278}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">By Ohm\u2019s Law,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">I = V\/Rp<\/span> <span data-contrast=\"none\">&#8230;<\/span> <span data-contrast=\"none\">(2)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259,&quot;469777462&quot;:[2421,3403],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[1,4]}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Where Rp is the combined resistance of the resistors in parallel.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<table data-tablestyle=\"MsoNormalTable\" data-tablelook=\"0\" aria-rowcount=\"4\">\n<tbody>\n<tr aria-rowindex=\"1\">\n<td data-celllook=\"4369\"><span data-contrast=\"none\">Also,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:240,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/td>\n<td data-celllook=\"4369\"><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"2\">\n<td data-celllook=\"4369\"><span data-contrast=\"none\">I1 = V\/R1&#8230;<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:240,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259,&quot;469777462&quot;:[1848],&quot;469777927&quot;:[0],&quot;469777928&quot;:[4]}\"> <\/span><\/td>\n<td data-celllook=\"4369\"><span data-contrast=\"none\">(3)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:3,&quot;335551620&quot;:3,&quot;335559737&quot;:6957,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"3\">\n<td data-celllook=\"4369\"><span data-contrast=\"none\">I2 = V\/R2&#8230;<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:240,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259,&quot;469777462&quot;:[1848],&quot;469777927&quot;:[0],&quot;469777928&quot;:[4]}\"> <\/span><\/td>\n<td data-celllook=\"4369\"><span data-contrast=\"none\">(4)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:3,&quot;335551620&quot;:3,&quot;335559737&quot;:6957,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"4\">\n<td data-celllook=\"4369\"><span data-contrast=\"none\">I3 = V\/R3&#8230;<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:240,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259,&quot;469777462&quot;:[1848],&quot;469777927&quot;:[0],&quot;469777928&quot;:[4]}\"> <\/span><\/td>\n<td data-celllook=\"4369\"><span data-contrast=\"none\">(5)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:3,&quot;335551620&quot;:3,&quot;335559737&quot;:6957,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span data-contrast=\"none\">The potential difference across each resistor will be the same as that of the battery. Substituting equations (2), (3), (4), and (5) in (1),<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:20}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V\/Rp = V\/R1 + V\/R2 + V\/R3<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 1\/Rp= 1\/R1 + 1\/R2 + 1\/R3<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:295}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Thus, when resistors are connected in parallel, the reciprocal of the equivalent resistance Rp is equal to the sum of the reciprocals of the individual resistances.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559737&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559737&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Solved Examples on Equivalent Resistance Formula: <\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559737&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Example 1: <\/span><\/b><span data-contrast=\"none\">As shown in the figure, two resistors with resistances 10 \u2126 and 15 \u2126 are connected to a 5 V battery. Find the:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Calibri&quot;,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Total resistance of the circuit<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:264}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Calibri&quot;,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Potential difference across the 15 Ohms resistor<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:264}\"> <\/span><\/li>\n<\/ol>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:2789,&quot;335559737&quot;:2789,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"><img loading=\"lazy\" class=\"alignnone size-medium wp-image-628258\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-162102-300x206.png\" alt=\"\" width=\"300\" height=\"206\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-162102-300x206.png?v=1687517678 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-162102.png?v=1687517678 316w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/> <\/span><\/p>\n<p>Figure 1<\/p>\n<p><b><span data-contrast=\"none\">Given:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:199}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Resistance (R1) = 10 \u2126 Resistance (R2) = 15 \u2126 Potential difference (V) = 5 V<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:6480,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:412}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">To find:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:211}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Tahoma\" data-listid=\"3\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Tahoma&quot;,&quot;469769242&quot;:[65533,2],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;multilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Total resistance of the circuit (Rs)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:240,&quot;469777462&quot;:[576,792],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[0,6]}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Tahoma\" data-listid=\"3\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Tahoma&quot;,&quot;469769242&quot;:[65533,2],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;multilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Potential difference across the 15 Ohms resistor (V2)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:240,&quot;469777462&quot;:[576,792],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[0,6]}\"> <\/span><\/li>\n<\/ol>\n<p><b><span data-contrast=\"none\">Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:199}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Tahoma\" data-listid=\"5\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Tahoma&quot;,&quot;469769242&quot;:[65533,2],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;multilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Rs = R1 + R2<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:192,&quot;469777462&quot;:[504,720],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[0,6]}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Tahoma\" data-listid=\"5\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Tahoma&quot;,&quot;469769242&quot;:[65533,2],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;multilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">V2 = IR2<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:216,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:187,&quot;469777462&quot;:[504,720],&quot;469777927&quot;:[0,0],&quot;469777928&quot;:[0,6]}\"> <\/span><\/li>\n<\/ol>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:242}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Solution:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:242}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">From the circuit diagram, the two resistors are connected in series. \u2234 Total Resistance of the circuit is given by<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559737&quot;:2880,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:376}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Rs = R1 + R2 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 Rs = 10 + 15 = 25 \u2126<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 Rs = 25 \u2126<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the total resistance of the circuit is 25 \u2126 . <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Applying Ohm\u2019s law to the entire circuit,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">V = IRs <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 5 = I \u2715 25 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 I = 5\/25 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 I = 0.2 A<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">When resistors are connected in series, the current flowing in the circuit will be the same at every point in the circuit.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, by using Ohm\u2019s law, V2 = IR2 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u2234 V2 = 0.2 x 15 = 3V <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the potential difference across the 15 Ohms resistor is 3V.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:214}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Example 2: <\/span><\/b><span data-contrast=\"none\">Consider a circuit with three resistors connected in series: R1 = 10 ohms, R2 = 20 ohms, and R3 = 30 ohms. Calculate the equivalent resistance of the circuit.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Solution: To find the equivalent resistance of resistors in series, we simply add up their individual resistances. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">R_eq = R1 + R2 + R3 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">R_eq = 10 + 20 + 30 <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">R_eq = 60 ohms<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the equivalent resistance of the circuit is 60 ohms.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Frequently Asked Questions on Equivalent Resistance Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">1: How do you find the equivalent resistance of parallel?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: To find the equivalent resistance of resistors connected in parallel, use the formula:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">1\/Req = 1\/R1 + 1\/R2 + 1\/R3 + &#8230;<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">where Req is the equivalent resistance and R1, R2, R3, &#8230; are the individual resistances in parallel. In other words, calculate the reciprocal of each resistance, sum them up, and take the reciprocal of the sum to obtain the equivalent resistance.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">2: Why is equivalent resistance less in parallel?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: In a parallel connection of resistors, the current divides among the branches, resulting in a lower equivalent resistance compared to a series connection. Each resistor in parallel has the same voltage across it, but the current is divided based on the resistances. According to Ohm&#8217;s Law, lower resistance allows for a larger current to flow. In a parallel circuit, the branches with lower resistance offer less opposition, allowing more current to flow through them. This combined effect of multiple paths for current flow leads to a lower total resistance in a parallel connection.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">3: What is equivalent resistance?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The equivalent resistance is the combined resistance of multiple resistors in a circuit. It represents a single resistor that would have the same effect on current flow as the combination of all the individual resistors. The equivalent resistance can be found by summing the resistances in series or using the reciprocal of the sum of reciprocals in parallel.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">4: What is the equivalent resistance formula of series and parallel?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The formula for calculating the equivalent resistance in a series connection is obtained by summing the individual resistances: Rs = R1 + R2 + R3 + &#8230; In a parallel connection, the formula involves taking the reciprocal of the sum of the reciprocals of the individual resistances: Rp = (1\/R1 + 1\/R2 + 1\/R3 + <\/span><span data-contrast=\"none\">&#8230;)-1<\/span><span data-contrast=\"none\">.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">5: What is the equivalent resistance formula for 2 resistors in parallel?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The formula for calculating the equivalent resistance of two resistors in parallel is given by: Rp = (R1 x R2) \/ (R1 + R2). This formula takes into account the reciprocals of the resistances and their sum to determine the overall resistance of the parallel combination of resistors.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">6: What is the total resistance for two 2-ohm resistors connected in parallel?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: When two 2-ohm resistors are connected in parallel, the total resistance can be calculated using the formula Rp = (R1 x R2) \/ (R1 + R2). Substituting the values, we get Rp = (2 x 2) \/ (2 + 2) = 4\/4 = 1 ohm. Therefore, the total resistance for two 2-ohm resistors connected in parallel is 1 ohm.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">7: What is the best way to find equivalent resistance?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The best way to find the equivalent resistance in a circuit depends on the specific circuit configuration.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">If the circuit consists of resistors connected in series and parallel, the best approach is to simplify the circuit step-by-step. Start by identifying resistors that are in series and calculate their equivalent resistance using the series formula (R_eq = R1 + R2 + &#8230;). Then, identify resistors in parallel and calculate their equivalent resistance using the parallel formula (1\/R_eq = 1\/R1 + 1\/R2 + &#8230;). Repeat this process until you have simplified the entire circuit into a single equivalent resistance.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">8: Which kind of connection will have higher equivalent resistance?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: In a series connection of resistors, the equivalent resistance is obtained by summing the individual resistances, resulting in a higher overall resistance than a parallel connection. In series, the same current flows through each resistor, while in parallel, the voltage across each resistor is the same. The reciprocal of the sum of the reciprocals of the individual resistances gives the equivalent resistance in parallel, which is always smaller than the smallest individual resistance. Thus, a series connection yields a higher equivalent resistance compared to a parallel connection when using the same set of resistors.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">9: What is the unit of equivalent resistance?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The unit of equivalent resistance is the same as the unit of resistance, which is the ohm (\u03a9). The ohm is the standard unit of electrical resistance in the International System of Units (SI).<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The ohm is represented by the symbol \u03a9 and is named after the German physicist Georg Simon Ohm. It is defined as the resistance between two points in a conductor when a constant current of one ampere (A) is flowing through it, producing a potential difference of one volt (V) across the conductor.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, when calculating the equivalent resistance of a circuit, the resulting value will be expressed in ohms (\u03a9). This unit indicates the level of opposition to the flow of electric current offered by the circuit or component.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">10: Is equivalent resistance the same as individual resistance?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: No, the equivalent resistance is not the same as the individual resistance of a single resistor in a circuit. The equivalent resistance refers to the single resistance value that would replace a combination of resistors in a circuit while maintaining the same overall effect on current flow.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">When resistors are connected in different configurations (such as series or parallel), their individual resistances combine to create an overall effect on the circuit. The equivalent resistance represents this combined effect and simplifies the circuit analysis by reducing multiple resistors to a single equivalent resistor.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction: Equivalent resistance formulas are used in electrical circuits to simplify complex circuits into a single equivalent resistance. The equivalent [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Equivalent Resistance Formula\u00a0","_yoast_wpseo_title":"Equivalent Resistance Formula\u00a0how to calculate total resistance","_yoast_wpseo_metadesc":"Understand how to calculate total resistance in a circuit by combining resistors in series and parallel configurations for efficient electrical calculations","custom_permalink":""},"categories":[8438,8521],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equivalent Resistance Formula\u00a0how to calculate total resistance<\/title>\n<meta name=\"description\" content=\"Understand how to calculate total resistance in a circuit by combining resistors in series and parallel configurations for efficient 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