{"id":1567,"date":"2017-09-04T08:00:03","date_gmt":"2017-09-04T15:00:03","guid":{"rendered":"http:\/\/www.autodesk.com\/products\/eagle\/blog\/?p=1567"},"modified":"2025-08-21T07:30:07","modified_gmt":"2025-08-21T14:30:07","slug":"kirchhoffs-law-for-complex-circuits","status":"publish","type":"post","link":"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/kirchhoffs-law-for-complex-circuits\/","title":{"rendered":"Using Kirchhoff\u2019s Law for Complex Circuits"},"content":{"rendered":"\n<p><em>Learn how to analyze a complex electrical circuit to find voltages of currents with Kirchhoff\u2019s Current Law and Voltage Law.<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"687\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL-1024x687.jpg\" alt=\"Kirchhoff's law\" class=\"wp-image-53292\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL-1024x687.jpg 1024w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL-300x201.jpg 300w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL-768x516.jpg 768w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL-1536x1031.jpg 1536w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-and-IL.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Ohm\u2019s Law is your golden ticket for calculating the voltage, current, or resistance in a simple series or parallel circuit, but what happens when your circuit is more complicated? You might be designing electronics that have both parallel and series resistance, and Ohm\u2019s Law starts to fall down. In such cases, a circuit diagram becomes essential for visualizing the arrangement of components and understanding how current and voltage are distributed throughout the circuit. Or what if you don\u2019t have a constant current source? In these situations, when you can\u2019t only use V = IR, it\u2019s time to stand on the shoulders of Ohm and use Kirchhoff\u2019s Circuit Law. Here we\u2019ll be looking at what Kirchhoff\u2019s Circuit Law is and how to use it to analyze the voltage and current of complex electrical circuits. Kirchhoff&#8217;s Laws are a basic tool in electrical engineering, providing the foundation for analyzing and solving circuits of any complexity.<\/span><\/p>\n\n\n\n<?php\nfunction autodesk_fusion_cta_horizontal() {\n    ob_start();\n    ?>\n    <style>\n        .cta-section-horizontal {\n            background: #ddd; \/* Much lighter grey background *\/\n            padding: 12px; \/* Adjusted padding *\/\n            border-radius: 8px;\n            box-shadow: 0 3px 5px rgba(0, 0, 0, 0.2);\n            color: #333; \/* Darker text color for better readability *\/\n            display: flex;\n            align-items: center;\n            justify-content: space-between;\n            max-width: 650px; \/* Width adjusted for a more compact look *\/\n            margin: 20px auto;\n            position: relative;\n            flex-wrap: nowrap; \/* Prevent wrapping *\/\n        }\n\n        .cta-section-horizontal img {\n            width: 60px; \/* Slightly larger logo *\/\n            height: auto; \/* Maintain aspect ratio *\/\n            margin-right: 12px; \/* Adjusted spacing *\/\n            background-color: #ddd; \/* Match the background color *\/\n            padding: 6px; \/* Adjusted padding *\/\n            border-radius: 8px; \/* Slightly rounding to match container *\/\n            box-shadow: 0 0 0 4px #ddd; \/* Blend with background *\/\n        }\n\n        .cta-text {\n            flex: 1;\n            margin-right: 12px; \/* Adjusted spacing *\/\n        }\n\n        .cta-title {\n            font-size: 18px; \/* Slightly larger title font size *\/\n            font-weight: bold; \/* Bold title *\/\n            color: #f9a825; \/* Orange color *\/\n            margin-bottom: 4px; \/* Reduced margin *\/\n        }\n\n        .cta-info {\n            display: none; \/* Hide description *\/\n        }\n\n        .cta-buttons {\n            display: flex;\n            gap: 8px; \/* Adjusted button spacing *\/\n            align-items: center;\n        }\n\n        .cta-button {\n            padding: 8px 12px; \/* Button padding *\/\n            font-size: 12px; \/* Smaller font size for buttons *\/\n            font-weight: bold;\n            text-transform: uppercase;\n            border-radius: 4px; \/* Slightly rounded corners *\/\n            border: 2px solid transparent;\n            cursor: pointer;\n            transition: all 0.3s ease;\n            display: inline-flex; \/* Use inline-flex to ensure proper alignment *\/\n            align-items: center; \/* Center align text vertically *\/\n            justify-content: center; \/* Center align text horizontally *\/\n            text-decoration: none !important; \/* Ensure no underlines with !important *\/\n            color: inherit; \/* Use the button's text color *\/\n        }\n\n        .cta-button.white-button {\n            background-color: #fff;\n            color: #333;\n            border: 2px solid #ddd;\n        }\n\n        .cta-button.white-button:hover {\n            background-color: #333;\n            color: #fff;\n            border: 2px solid #f9a825;\n        }\n\n        .cta-button.black-button {\n            background-color: #f9a825;\n            color: #fff;\n            border: 2px solid #f9a825;\n        }\n\n        .cta-button.black-button:hover {\n            background-color: #fff;\n            color: #f9a825;\n            border: 2px solid #fff;\n        }\n    <\/style>\n\n    <div class=\"cta-section-horizontal\">\n        <img decoding=\"async\" src=\"https:\/\/autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/09\/autodesk-fusion-product-icon-400.png\" alt=\"Autodesk Fusion Logo\">\n        <div class=\"cta-text\">\n            <h1 class=\"cta-title\">Elevate your design and manufacturing processes with Autodesk Fusion<\/h1>\n        <\/div>\n        <div class=\"cta-buttons\">\n            <a href=\"https:\/\/www.autodesk.com\/products\/fusion-360\/trial-intake-flow\" class=\"cta-button white-button\">Get a 30-Day Free Trial<\/a>\n            <a href=\"https:\/\/www.autodesk.com\/products\/fusion-360\/extensions\" class=\"cta-button black-button\">See Plans and Pricing<\/a>\n        <\/div>\n    <\/div>\n\n    <?php\n    return ob_get_clean();\n}\nadd_shortcode('autodesk_fusion_cta_horizontal', 'autodesk_fusion_cta_horizontal');\n?>\n\n\n<h2 class=\"wp-block-heading\" id=\"what-is-kirchhoffs-circuit-law\">What is Kirchhoff\u2019s Circuit Law?<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">When you\u2019re building a complex circuit that includes bridges or T networks, then you can\u2019t solely rely on Ohm\u2019s Law to find the voltage or current. This is where Kirchhoff&#8217;s Circuit Law comes in handy, which allows you to calculate the current and voltage for complex circuits with a system of linear equations. There are two variations of Kirchhoff&#8217;s Law, including:<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><b>Kirchhoff\u2019s Current Law:<\/b><span style=\"font-weight: 400;\"> To analyze the total current for a complex circuit <\/span><\/li>\n\n\n\n<li><b>Kirchhoff&#8217;s Voltage Law<\/b><span style=\"font-weight: 400;\">: To analyze the total voltage for a complex circuit<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">When you combine these two laws, you get <\/span><b>Kirchhoff\u2019s Circuit Law<\/b><\/li>\n<\/ul>\n\n\n\n<p>In circuits that contain two loops or more, both Kirchhoff&#8217;s Current Law and Kirchhoff&#8217;s Voltage Law are applied to analyze current and voltage throughout the network.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Like any other scientific or mathematical law named after its creator, Kirchhoff\u2019s Circuit Law was invented by <\/span><a href=\"https:\/\/www.britannica.com\/biography\/Gustav-Robert-Kirchhoff\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"font-weight: 400;\">German Physicist Gustav Kirchhoff<\/span><\/a><span style=\"font-weight: 400;\">. Gustav was known for many achievements in his lifetime, including the theory of spectrum analysis, which proved that elements give off a unique light pattern when heated. When Kirchhoff and chemist Robert Bunsen analyzed these light patterns through a prism, they discovered that each element in the periodic table has its own unique wavelength. The discovery of this pattern allowed the duo to uncover two new elements, cesium, and rubidium.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"473\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download-1024x473.png\" alt=\"\" class=\"wp-image-53286\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download-1024x473.png 1024w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download-300x138.png 300w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download-768x354.png 768w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download-1536x709.png 1536w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/download.png 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Kirchhoff later went on to apply his spectrum analysis theory to study the composition of the sun, where he discovered many dark lines in the sun\u2019s wavelength spectrum. This was caused by gas from the sun absorbing specific wavelengths of light, and this discovery marked the beginning of a new age of research and exploration in the field of astronomy.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">A bit closer to home in the world of electronics, Kirchhoff announced his set of laws for analyzing the current and voltage for electrical circuits in 1845, known today as Kirchhoff&#8217;s Circuit Law. This work builds upon the foundation outlined in Ohm\u2019s Law and has helped pave the way for the complex circuit analysis that we rely on today.<\/span><\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"understanding-volate-sources\">Understanding Volate Sources<\/h2>\n\n\n<p>Voltage sources are the heart of any electrical circuit, providing the driving force that pushes electric current through the various circuit elements. Whether you\u2019re working with a simple battery or a sophisticated power supply, the voltage source establishes the potential difference needed for current to flow through the components and wires connecting your circuit. In the context of Kirchhoff\u2019s laws, understanding how voltage sources interact with other components is essential for accurate circuit analysis.<\/p>\n\n\n\n<p>When you apply Kirchhoff\u2019s voltage law (also known as the voltage law or loop rule), you must account for every voltage source in the circuit. Each voltage source contributes a voltage rise, which is balanced by the voltage drops across resistors and other components as you move around a closed loop. This balance ensures that the algebraic sum of all voltages in any closed loop is equal to zero, a fundamental principle for analyzing both simple and complex circuits.<\/p>\n\n\n\n<p>Voltage sources can be found in all types of circuits, from basic DC circuits powered by a single battery to more complex AC circuits with multiple voltage sources and loads. By carefully considering the placement and value of each voltage source, you can predict how current will flow and how voltages will be distributed across the circuit. This understanding is crucial when you start analyzing circuits using Kirchhoff\u2019s laws, as it allows you to solve for unknown values and design circuits that perform as intended.<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"kirchhoffs-current-law\">Kirchhoff\u2019s Current Law<\/h2>\n\n\n<p><b>Kirchhoff\u2019s Current Law states that the amount of current that enters a node equals the amount of current leaving a node.<\/b><span style=\"font-weight: 400;\"> Why? Because when current enters a node, it has no other place to go except to exit. What goes in must come out. You can identify a node where two or more paths are connected via a common point. In a schematic, this will be the junction dot connecting two intersecting net connections. <\/span>When using <span style=\"font-weight: 400;\">Kirchoff\u2019s Current Law<\/span>, keep in mind that<span style=\"font-weight: 400;\"> everything has to balance out, a principle Kirchhoff called the <\/span><b>Conservation of Charge<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">To validate Kirchoff\u2019s Current Law in a circuit, <\/span>follow these three steps<span style=\"font-weight: 400;\">:<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Calculate the total current of the circuit<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Calculate the current flowing through each node<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Compare input and output currents at specific nodes to validate Kirchoff\u2019s Current Law.<\/span><\/li>\n<\/ol>\n\n\n\n<p>In more complex circuits, you may encounter specific nodes such as node B or junction E, where you apply Kirchhoff&#8217;s current law to analyze the currents flowing through each branch.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"1-calculate-the-total-current\">1. Calculate the total current<\/h3>\n\n\n<p><span style=\"font-weight: 400;\">Start by using Ohm\u2019s Law to get the total current of our circuit with <\/span><b>I = V\/R<\/b><span style=\"font-weight: 400;\">. We already have our total voltage, and now we just need to find the total resistance in all of our nodes. This requires the simple method of calculating the total resistance of resistors wired in parallel.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Once you have your total resistance for the entire circuit, <\/span>plug it<span style=\"font-weight: 400;\"> into Ohm\u2019s Law <\/span><b>I = V\/R<\/b><span style=\"font-weight: 400;\"> to get the total current in our circuit<\/span>.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"2-calculate-node-currents\">2. Calculate node currents<\/h3>\n\n\n<p><span style=\"font-weight: 400;\">Now that we know how many amps are flowing out of our circuit, we can calculate the current at each set of nodes. We\u2019ll again enlist the help of Ohm\u2019s Law in the form of <\/span><b>I = V\/R<\/b><span style=\"font-weight: 400;\"> to get the current for each node branch.<\/span><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"3-validate-kirchhoffs-current-law\">3. Validate Kirchhoff\u2019s Current Law<\/h3>\n\n\n<p><span style=\"font-weight: 400;\">With the current for each node branch calculated, we now have two distinct reference points that we can use to compare our input and output currents. This will allow us to analyze our circuit and validate Kirchhoff\u2019s Current Law<\/span>.<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"kirchhoffs-voltage-law\">Kirchhoff\u2019s Voltage Law<\/h2>\n\n\n<p><b>Kirchhoff\u2019s Voltage Law states that in any closed-loop circuit, the total voltage will always equal the sum of all the voltage drops within the loop.<\/b><span style=\"font-weight: 400;\"> You\u2019ll find voltage drops occurring whenever current flows through a passive component like a resistor, and Kirchhoff referred to this law as the <\/span><b>Conservation of Energy<\/b><span style=\"font-weight: 400;\">. Again, what goes in must come out.<\/span><\/p>\n\n\n\n<p>When applying Kirchhoff&#8217;s Voltage Law, you analyze loops in the circuit. The loop starts at a chosen point and proceeds in a specified direction, either clockwise or counterclockwise. It is important to maintain the same direction throughout the loop to ensure correct voltage summation. The directions you choose for current flow and voltage arrows must be consistent. If you traverse a component in the direction opposite to the current flow, the voltage drop is considered negative; if you go in the same direction as the current, the voltage drop is positive. This sign convention helps determine the actual direction and polarity of voltages and currents in the circuit.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">If your circuits&#8217; passive components are connected in series, you can simply add the total voltage drops together and compare it to the total voltage to validate the law.<\/span> <span style=\"font-weight: 400;\">Since the total voltage drop in the circuit has to equal the total voltage source, this provides an easy way to calculate our missing variable. If you wanted to express this relationship as a proper algebraic expression, you\u2019d get the sum of all voltage drops and the total voltage equalling zero, as shown here:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"815\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-1024x815.png\" alt=\"Kirchhoffs Voltage Law\" class=\"wp-image-53297\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-1024x815.png 1024w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-300x239.png 300w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-768x611.png 768w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL-1536x1223.png 1536w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/02\/Kirchhoff-VL.png 1838w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Ohm&#8217;s Law is often used together with Kirchhoff&#8217;s Law to analyze current flow and voltage drops in the circuit. This combination allows you to solve for unknown currents and voltages throughout the loops.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Typically you&#8217;ll need to take the following steps to validate Kirchoff\u2019s Voltage Law:<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Calculate the <\/span><b>total resistance<\/b><span style=\"font-weight: 400;\"> of the circuit<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Calculate the <\/span><b>total current<\/b><span style=\"font-weight: 400;\"> of the circuit<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Calculate the <\/span><b>current through<\/b><span style=\"font-weight: 400;\"> each resistor<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Calculate the <\/span><b>voltage drop across<\/b><span style=\"font-weight: 400;\"> each resistor<\/span><\/li>\n<\/ol>\n\n\n\n<p><span style=\"font-weight: 400;\">Compare the<\/span><b> voltage source to the total voltage drop<\/b><span style=\"font-weight: 400;\"> to validate Kirchoff\u2019s Voltage Law<\/span><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"1-calculate-the-total-resistance\">1. Calculate the total resistance<\/h3>\n\n\n<p>If all of your resistors are wired in series, you can easily find the total resistance by just adding all of the resistance values together. This total resistance is also known as the equivalent resistance of the series circuit.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"2-calculate-the-total-current\">2. Calculate the total current<\/h3>\n\n\n<p>Now that we know our total resistance, we can again use Ohm\u2019s Law to get the total current of our circuit in the form of <strong>I = V\/R,<\/strong> which looks like this: This is an example of setting up an equation to solve for the total current in the circuit.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"3-calculate-the-current-through-each-resistor\">3. Calculate the current through each resistor<\/h3>\n\n\n<p>If all of your resistors are wired in series, they\u2018 wi\u2018ll all have the same amount of current flowing through them, which we can express as:<\/p>\n\n\n\n<p>This approach can also be applied to individual components in the circuit, such as resistors, capacitors, and inductors, by using the equations specific to each individual component.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"4-calculate-the-voltage-drop-across-each-resistor\">4. Calculate the voltage drop across each resistor<\/h3>\n\n\n<p>Our final calculation will again use Ohm\u2019s Law to give us the total voltage drop for each resistor in the form of <strong>V = IR<\/strong>, which looks like this:<\/p>\n\n\n\n<p>A negative sign in the result indicates that the voltage drop is in the direction opposite to the chosen reference direction.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"5-validate-kirchoffs-voltage-law\">5. Validate Kirchoff\u2019s Voltage Law<\/h3>\n\n\n<p>To see Kirchhoff\u2019s voltage law in action, let\u2019s walk through a practical example using a simple series circuit. Imagine you have a circuit with a single voltage source\u2014a 12V battery\u2014and three resistors: 2\u03a9, 3\u03a9, and 5\u03a9, all connected in series. The voltage source provides the energy, and as current flows through each resistor, a voltage drop occurs across each one.<\/p>\n\n\n\n<p>First, calculate the total resistance in the circuit by adding up the resistances: 2\u03a9 + 3\u03a9 + 5\u03a9 = 10\u03a9. Next, use Ohm\u2019s law to find the current flowing through the circuit: I = V\/R = 12V\/10\u03a9 = 1.2A. Since the resistors are in series, the same current flows through each resistor.<\/p>\n\n\n\n<p>Now we have all of the data we need, including the total voltage of our circuit, along with each voltage drop across each of our resistors. When putting all of this together, we can easily validate Kirchhoff\u2019s Voltage Law. The total voltage equals the total voltage drop in our circuit. This validation is performed by summing the voltages around all loops in the circuit. What goes in must come out, and Kirchoff\u2019s Law works yet again!<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"process-for-using-kirchhoffs-circuit-law\">Process for Using Kirchhoff\u2019s Circuit Law<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">With an understanding of how Kirchhoff\u2019s Circuit Law works, you now have a new tool in your toolbox for analyzing voltage and current in complete circuits. When using these Laws out in the wild, consider using the following step-by-step process:<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">First, begin by labeling all of the known voltages and resistances on your circuit.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Then name each branch on your circuit with a current label, such as <\/span><span style=\"font-weight: 400;\">I1, I2, I3,<\/span><span style=\"font-weight: 400;\"> etc.&nbsp;A branch is a single or group of components connected between two nodes.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Next, find Kirchhoff\u2019s Current Law for each node in your circuit.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Then find Kirchhoff&#8217;s Voltage Law for each independent loop in your circuit.<\/span><\/li>\n<\/ol>\n\n\n\n<p><span style=\"font-weight: 400;\">Once you have Kirchoff\u2019s Current and Voltage Laws calculated, you can then use your equations to find any missing currents. Ready to try it on your own? Take a look at the circuit below and see if you can validate Kirchoff\u2019s Current Law and Voltage Law with a little bit of help from Ohm!<\/span><\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"standing-on-the-shoulders-of-ohm\">Standing on the shoulders of Ohm<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">With Kirchhoff\u2019s Circuit Law in hand, you now have all the tools you need to analyze the voltage and current for complex circuits. Like many other scientific and mathematical principles, Kirchhoff\u2019s Law stands on the shoulders of what came before it &#8211; Ohm\u2019s Law. You\u2019ll find yourself using Ohm\u2019s Law to calculate individual resistances, voltages, or currents and then building upon these calculations with Kirchhoff\u2019s Law to see if your circuit holds true to these Current and Voltage principles.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Ready to apply Kirchhoff\u2019s Law in your own electronics design project? Try Autodesk Fusion for free today!<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Learn how to analyze a complex electrical circuit to find voltages of currents with Kirchhoff\u2019s Current Law and Voltage Law.<\/p>\n","protected":false},"author":3911,"featured_media":53292,"menu_order":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[359],"tags":[207,360,206],"coauthors":[589],"class_list":["post-1567","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics-engineering","tag-electronics","tag-electronics-engineer","tag-pcb","dhig-theme--light"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Using Kirchhoff\u2019s Law for Complex Circuits - Fusion Blog<\/title>\n<meta name=\"description\" content=\"Learn how to analyze a complex electrical circuit to find voltages of currents with Kirchhoff\u2019s Current Law and Voltage Law.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/kirchhoffs-law-for-complex-circuits\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Using Kirchhoff\u2019s Law for Complex Circuits - 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