{"id":3382,"date":"2026-08-23T14:56:58","date_gmt":"2026-08-23T14:56:58","guid":{"rendered":"https:\/\/us.allassignmentsupport.com\/blog\/?p=3382"},"modified":"2026-08-23T15:13:58","modified_gmt":"2026-08-23T15:13:58","slug":"kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students","status":"publish","type":"post","link":"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/","title":{"rendered":"Kirchhoff&#8217;s Laws and Circuit Analysis: A Step-by-Step Guide for Physics Students"},"content":{"rendered":"<p dir=\"ltr\">Simple series and parallel circuits feel manageable, but the moment a circuit has multiple loops and multiple batteries, most students freeze \u2014 it&#8217;s no longer obvious which direction current flows, or which equations to even write down. Kirchhoff&#8217;s laws are the systematic tool that solves this, but the process of <em>setting up<\/em> the equations (not just knowing the laws exist) is where assignments are actually won or lost. This guide walks through both laws individually, then works through a full multi-loop circuit from start to finish.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-light-blue 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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#Kirchhoffs_Two_Laws_Precisely_Stated\" title=\"Kirchhoff&#8217;s Two Laws, Precisely Stated\">Kirchhoff&#8217;s Two Laws, Precisely Stated<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#Setting_Up_a_Circuit_Problem_The_Method\" title=\"Setting Up a Circuit Problem: The Method\">Setting Up a Circuit Problem: The Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#Worked_Example_1_Single-Loop_Circuit_Building_the_Method\" title=\"Worked Example 1: Single-Loop Circuit (Building the Method)\">Worked Example 1: Single-Loop Circuit (Building the Method)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#Worked_Example_2_Two-Loop_Circuit_Full_Kirchhoffs_Laws_Application\" title=\"Worked Example 2: Two-Loop Circuit (Full Kirchhoff&#8217;s Laws Application)\">Worked Example 2: Two-Loop Circuit (Full Kirchhoff&#8217;s Laws Application)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#Worked_Example_3_Resistors_in_Series_and_Parallel_A_Shortcut_Before_Reaching_for_Kirchhoffs_Laws\" title=\"Worked Example 3: Resistors in Series and Parallel (A Shortcut Before Reaching for Kirchhoff&#8217;s Laws)\">Worked Example 3: Resistors in Series and Parallel (A Shortcut Before Reaching for Kirchhoff&#8217;s Laws)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#When_SeriesParallel_Shortcuts_Dont_Work_%E2%80%94_And_Kirchhoffs_Laws_Are_Required\" title=\"When Series\/Parallel Shortcuts Don&#8217;t Work \u2014 And Kirchhoff&#8217;s Laws Are Required\">When Series\/Parallel Shortcuts Don&#8217;t Work \u2014 And Kirchhoff&#8217;s Laws Are Required<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#A_Step-by-Step_Checklist_for_Students_Stuck_on_a_Kirchhoffs_Laws_Problem\" title=\"A Step-by-Step Checklist for Students Stuck on a Kirchhoff&#8217;s Laws Problem\">A Step-by-Step Checklist for Students Stuck on a Kirchhoff&#8217;s Laws Problem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/us.allassignmentsupport.com\/blog\/kirchhoffs-laws-and-circuit-analysis-a-step-by-step-guide-for-physics-students\/#FAQs\" title=\"FAQs\">FAQs<\/a><\/li><\/ul><\/nav><\/div>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Kirchhoffs_Two_Laws_Precisely_Stated\"><\/span>Kirchhoff&#8217;s Two Laws, Precisely Stated<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><strong>Kirchhoff&#8217;s Current Law (KCL):<\/strong> The sum of currents entering a junction equals the sum of currents leaving it. This is simply a statement of charge conservation \u2014 charge can&#8217;t pile up or disappear at a junction.<\/p>\n<p dir=\"ltr\"><strong>Kirchhoff&#8217;s Voltage Law (KVL):<\/strong> The sum of voltage changes around any closed loop in a circuit equals zero \u2014 conceptually the electrical version of the <strong><a href=\"https:\/\/us.allassignmentsupport.com\/blog\/work-energy-and-power-in-physics-formulas-and-worked-examples\/\">conservation of energy<\/a><\/strong> principle applied to a charge traveling around a complete loop and returning to its starting point with no net change in potential energy.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Setting_Up_a_Circuit_Problem_The_Method\"><\/span>Setting Up a Circuit Problem: The Method<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol dir=\"ltr\">\n<li><strong>Label every current<\/strong> in the circuit with a symbol (I\u2081, I\u2082, I\u2083&#8230;) and an assumed direction (an arrow). If you guess the direction wrong, the math will simply give you a negative value for that current \u2014 this is completely fine and doesn&#8217;t mean you made an error.<\/li>\n<li><strong>Apply KCL at junctions<\/strong> where currents split or combine, writing one equation per independent junction.<\/li>\n<li><strong>Apply KVL around loops<\/strong>, choosing a direction to &#8220;walk&#8221; around each loop and tracking voltage rises and drops as you cross each component.<\/li>\n<li><strong>Sign convention for KVL:<\/strong> When walking through a resistor in the <em>same<\/em> direction as your assumed current, the voltage drops (subtract IR). When walking through a battery from \u2212 to + terminal, the voltage rises (add EMF); from + to \u2212 terminal, it drops (subtract EMF).<\/li>\n<li><strong>Solve the resulting system of equations<\/strong> simultaneously.<\/li>\n<\/ol>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Worked_Example_1_Single-Loop_Circuit_Building_the_Method\"><\/span>Worked Example 1: Single-Loop Circuit (Building the Method)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><strong>Problem:<\/strong> A single loop contains a 12V battery and two resistors in series, R\u2081 = 4\u03a9 and R\u2082 = 8\u03a9. Find the current in the circuit.<\/p>\n<p dir=\"ltr\"><strong>Step 1 \u2014 Label current:<\/strong> Assume current I flows clockwise.<\/p>\n<p dir=\"ltr\"><strong>Step 2 \u2014 Apply KVL<\/strong>, walking clockwise starting just after the battery&#8217;s negative terminal: +12 \u2212 I(4) \u2212 I(8) = 0<\/p>\n<p dir=\"ltr\"><strong>Step 3 \u2014 Solve:<\/strong> 12 = 12I I = 1 A<\/p>\n<p dir=\"ltr\"><strong>Answer:<\/strong> The current is 1 A, flowing in the assumed clockwise direction (positive result confirms the assumed direction was correct).<\/p>\n<p dir=\"ltr\"><strong>Common mistake to avoid:<\/strong> Getting the sign of the battery term wrong. Walking from the \u2212 to + terminal of a battery is a voltage <em>rise<\/em> (positive in the equation); walking the other way is a voltage <em>drop<\/em> (negative). Getting this reversed is the single most common sign error in single-loop KVL problems.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Worked_Example_2_Two-Loop_Circuit_Full_Kirchhoffs_Laws_Application\"><\/span>Worked Example 2: Two-Loop Circuit (Full Kirchhoff&#8217;s Laws Application)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><strong>Problem:<\/strong> A circuit has two loops sharing a middle branch. The left loop contains a 10V battery and resistor R\u2081 = 2\u03a9. The right loop contains a 6V battery and resistor R\u2082 = 3\u03a9. The shared middle branch contains resistor R\u2083 = 5\u03a9. Find the current through each resistor.<\/p>\n<p dir=\"ltr\"><strong>Step 1 \u2014 Label currents:<\/strong> Let I\u2081 flow through R\u2081 (left loop, clockwise), I\u2082 flow through R\u2082 (right loop, clockwise), and I\u2083 flow through R\u2083 (the shared middle branch, assumed downward).<\/p>\n<p dir=\"ltr\"><strong>Step 2 \u2014 Apply KCL at the top junction<\/strong> (where the three branches meet): I\u2081 = I\u2082 + I\u2083 &#8230; (Equation 1)<\/p>\n<p dir=\"ltr\"><em>(This assumes I\u2081 flows into the junction, and both I\u2082 and I\u2083 flow out \u2014 the specific assumed directions depend on the circuit diagram, but the key skill is writing one KCL equation per independent junction.)<\/em><\/p>\n<p dir=\"ltr\"><strong>Step 3 \u2014 Apply KVL to the left loop<\/strong> (walking clockwise: through the 10V battery from \u2212 to + is a rise, through R\u2081 is a drop, through R\u2083 is a drop since I\u2083 flows in the same direction as our walk): 10 \u2212 I\u2081(2) \u2212 I\u2083(5) = 0 &#8230; (Equation 2)<\/p>\n<p dir=\"ltr\"><strong>Step 4 \u2014 Apply KVL to the right loop<\/strong> (walking clockwise: through R\u2083 against the assumed I\u2083 direction is a rise, through R\u2082 is a drop, through the 6V battery from + to \u2212 is a drop): \u2212I\u2083(5)(\u22121) \u2212 I\u2082(3) \u2212 6 = 0, which simplifies to: 5I\u2083 \u2212 3I\u2082 \u2212 6 = 0 &#8230; (Equation 3)<\/p>\n<p dir=\"ltr\"><strong>Step 5 \u2014 Substitute Equation 1 (I\u2081 = I\u2082 + I\u2083) into Equation 2:<\/strong> 10 \u2212 (I\u2082 + I\u2083)(2) \u2212 5I\u2083 = 0 10 \u2212 2I\u2082 \u2212 2I\u2083 \u2212 5I\u2083 = 0 10 \u2212 2I\u2082 \u2212 7I\u2083 = 0 &#8230; (Equation 2, revised)<\/p>\n<p dir=\"ltr\"><strong>Step 6 \u2014 Now solve Equations 2 (revised) and 3 simultaneously.<\/strong><\/p>\n<p dir=\"ltr\">From Equation 3: 5I\u2083 \u2212 3I\u2082 = 6, so I\u2082 = (5I\u2083 \u2212 6)\/3<\/p>\n<p dir=\"ltr\">Substituting into Equation 2 (revised): 10 \u2212 2[(5I\u2083 \u2212 6)\/3] \u2212 7I\u2083 = 0 Multiply through by 3: 30 \u2212 2(5I\u2083 \u2212 6) \u2212 21I\u2083 = 0 30 \u2212 10I\u2083 + 12 \u2212 21I\u2083 = 0 42 \u2212 31I\u2083 = 0 I\u2083 = 42\/31 \u2248 1.35 A<\/p>\n<p dir=\"ltr\"><strong>Step 7 \u2014 Back-substitute to find I\u2082 and I\u2081:<\/strong> I\u2082 = (5(1.35) \u2212 6)\/3 = (6.75 \u2212 6)\/3 = 0.75\/3 = 0.25 A I\u2081 = I\u2082 + I\u2083 = 0.25 + 1.35 = 1.60 A<\/p>\n<p dir=\"ltr\"><strong>Answer:<\/strong> I\u2081 \u2248 1.60 A, I\u2082 \u2248 0.25 A, I\u2083 \u2248 1.35 A.<\/p>\n<p dir=\"ltr\"><strong>Common mistake to avoid:<\/strong> Trying to solve all three equations independently without substitution. Multi-loop circuits always produce a system of simultaneous equations \u2014 the practical skill being tested is careful algebraic substitution to reduce three unknowns down to one, not any new physics concept beyond the two laws themselves.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Worked_Example_3_Resistors_in_Series_and_Parallel_A_Shortcut_Before_Reaching_for_Kirchhoffs_Laws\"><\/span>Worked Example 3: Resistors in Series and Parallel (A Shortcut Before Reaching for Kirchhoff&#8217;s Laws)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Before applying Kirchhoff&#8217;s laws to a complex circuit, it&#8217;s often worth checking whether parts of it can be simplified using series\/parallel combination rules first \u2014 this can turn a multi-loop problem into a much simpler single-loop one.<\/p>\n<p dir=\"ltr\"><strong>Series resistors:<\/strong> R_total = R\u2081 + R\u2082 + R\u2083 + &#8230; <strong>Parallel resistors:<\/strong> 1\/R_total = 1\/R\u2081 + 1\/R\u2082 + 1\/R\u2083 + &#8230;<\/p>\n<p dir=\"ltr\"><strong>Problem:<\/strong> A 20\u03a9 resistor is in parallel with a 30\u03a9 resistor, and this combination is in series with a 5\u03a9 resistor, all connected to a 24V battery. Find the total current supplied by the battery.<\/p>\n<p dir=\"ltr\"><strong>Step 1 \u2014 Combine the parallel resistors:<\/strong> 1\/R_parallel = 1\/20 + 1\/30 = 3\/60 + 2\/60 = 5\/60 R_parallel = 60\/5 = 12\u03a9<\/p>\n<p dir=\"ltr\"><strong>Step 2 \u2014 Add the series resistor:<\/strong> R_total = 12 + 5 = 17\u03a9<\/p>\n<p dir=\"ltr\"><strong>Step 3 \u2014 Apply Ohm&#8217;s Law:<\/strong> I = V\/R = 24\/17 \u2248 1.41 A<\/p>\n<p dir=\"ltr\"><strong>Answer:<\/strong> The battery supplies approximately 1.41 A.<\/p>\n<p dir=\"ltr\"><strong>Common mistake to avoid:<\/strong> Applying the series formula to resistors that are actually in parallel, or vice versa. A quick way to check: resistors are in parallel if both ends of each resistor connect to the same two nodes (same two points in the circuit); they&#8217;re in series if they share only one common node with no other branch connecting there.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"When_SeriesParallel_Shortcuts_Dont_Work_%E2%80%94_And_Kirchhoffs_Laws_Are_Required\"><\/span>When Series\/Parallel Shortcuts Don&#8217;t Work \u2014 And Kirchhoff&#8217;s Laws Are Required<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Series\/parallel simplification only works when resistors can be cleanly identified as sharing common nodes in a simple way. Circuits with multiple independent EMF sources (like the two-battery example above), or resistor networks that don&#8217;t reduce cleanly (such as a Wheatstone bridge configuration), require the full Kirchhoff&#8217;s laws approach shown in Worked Example 2, since there&#8217;s no way to combine them using simple series\/parallel rules alone.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"A_Step-by-Step_Checklist_for_Students_Stuck_on_a_Kirchhoffs_Laws_Problem\"><\/span>A Step-by-Step Checklist for Students Stuck on a Kirchhoff&#8217;s Laws Problem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol dir=\"ltr\">\n<li>First check whether series\/parallel combination rules can simplify part of the circuit \u2014 this can save significant time before resorting to the full Kirchhoff&#8217;s laws method.<\/li>\n<li>Label every unknown current with a symbol and an assumed direction \u2014 a wrong guess just produces a negative answer, which is fine.<\/li>\n<li>Write one KCL equation for each independent junction (a circuit with J junctions typically needs J \u2212 1 independent KCL equations).<\/li>\n<li>Write one KVL equation per independent loop, carefully tracking the sign convention: drops when walking through a resistor in the same direction as assumed current, rises when walking through a battery from \u2212 to + terminal.<\/li>\n<li>Use substitution to reduce the system of equations to one variable at a time, solving step by step rather than trying to solve everything simultaneously in one pass.<\/li>\n<\/ol>\n<p>Kirchhoff&#8217;s laws become especially challenging when a full assignment combines circuit analysis with Ohm&#8217;s law, electrical power, and experimental data. For students working through broader circuit-analysis coursework, our <a class=\"decorated-link\" href=\"https:\/\/us.allassignmentsupport.com\/physics-assignment-help\" target=\"_new\" rel=\"noopener\" data-start=\"565\" data-end=\"655\"><strong data-start=\"566\" data-end=\"593\">Physics Assignment Help<\/strong><\/a> service provides support across these physics topics.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\"><strong>Q1: What happens if I guess the wrong direction for a current?<\/strong> Nothing goes wrong with your method \u2014 if your assumed direction is incorrect, solving the equations will simply produce a negative value for that current, which tells you the actual current flows opposite to your assumed direction. The magnitude will still be correct as long as your equations were set up consistently.<\/p>\n<p dir=\"ltr\"><strong>Q2: How many KVL and KCL equations do I need for a given circuit?<\/strong> As a general rule, you need enough independent equations to match the number of unknown currents. For a circuit with J junctions and B independent loops, you&#8217;ll typically use (J \u2212 1) independent KCL equations and enough KVL equations (one per independent loop) to reach the total number of unknowns.<\/p>\n<p dir=\"ltr\"><strong>Q3: Why do I sometimes get a negative resistor voltage in my KVL equation?<\/strong> This happens naturally depending on which direction you&#8217;re &#8220;walking&#8221; around the loop relative to the assumed current direction through that resistor \u2014 walking in the same direction as the assumed current gives a voltage drop (negative in the sum), while walking against it gives a voltage rise (positive). This is a normal part of the sign convention, not an error.<\/p>\n<p dir=\"ltr\"><strong>Q4: When should I use series\/parallel simplification instead of full Kirchhoff&#8217;s laws?<\/strong> Use series\/parallel simplification whenever a circuit contains only resistors that can be clearly grouped as sharing common nodes in a simple pattern, and there&#8217;s only one EMF source (or sources that can be combined similarly). Once a circuit has multiple independent EMF sources or a more complex resistor network (like a bridge configuration), the full Kirchhoff&#8217;s laws method is necessary.<\/p>\n<p dir=\"ltr\"><strong>Q5: Is there a way to check my answer after solving a multi-loop circuit?<\/strong> Yes \u2014 substitute your solved current values back into all of the original KCL and KVL equations (not just the ones you used last) to confirm they all balance to zero or hold true. You can also do a quick sanity check using conservation of energy: the total power delivered by all batteries should equal the total power dissipated across all resistors.<\/p>\n<p dir=\"ltr\"><strong>Q6: How does this connect to other assignment work?<\/strong> Setting up and solving simultaneous equations here uses the same systematic, one-equation-per-unknown discipline as the free-body diagram method in <strong><a href=\"https:\/\/us.allassignmentsupport.com\/blog\/newtons-laws-of-motion-a-problem-solving-guide-with-worked-examples\/\">Newton&#8217;s Laws of Motion<\/a><\/strong>. If your circuit lab asks you to compare a measured current to a predicted one, reporting that comparison properly means applying the percent-error and propagation methods from <strong><a href=\"https:\/\/us.allassignmentsupport.com\/blog\/error-analysis-and-uncertainty-in-physics-lab-reports-a-complete-guide\/\">Error Analysis and Uncertainty in Physics Lab Reports<\/a><\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Simple series and parallel circuits feel manageable, but the moment a circuit has multiple loops and multiple batteries, most students [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":3385,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"none","_seopress_titles_title":"Kirchhoff's Laws and Circuit Analysis: A Step-by-Step Guide for Physics Students","_seopress_titles_desc":"A university-level guide to Kirchhoff's current and voltage laws, covering series and parallel circuits, and fully worked examples of multi-loop circuit analysis for physics students.","_seopress_robots_index":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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