{"id":1633,"date":"2022-07-21T06:18:50","date_gmt":"2022-07-21T13:18:50","guid":{"rendered":"http:\/\/www.autodesk.com\/products\/eagle\/blog\/?p=1633"},"modified":"2025-08-07T09:35:23","modified_gmt":"2025-08-07T16:35:23","slug":"use-thevenins-theorem","status":"publish","type":"post","link":"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/use-thevenins-theorem\/","title":{"rendered":"How to Use Thevenin\u2019s Theorem"},"content":{"rendered":"\n<p><em>Learn how to use Thevenin\u2019s Theorem to calculate current and voltage across a load resistor in a linear circuit.<\/em><\/p>\n\n\n\n<p>Tired of recalculating your entire circuit every time you change your load resistance? Thevenin\u2019s Theorem can help.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"494\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/leon-1024x494.jpg\" alt=\"Thevenin's Theorem\" class=\"wp-image-65431\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/leon-1024x494.jpg 1024w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/leon-300x145.jpg 300w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/leon-768x370.jpg 768w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/leon.jpg 1078w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/www.atlearner.com\/2019\/07\/Thevenin-theorem.html\">Image Source<\/a><\/figcaption><\/figure>\n\n\n<h2 class=\"wp-block-heading\" id=\"how-to-calculate-load-current-and-voltage-with-thevenins-theorem\">How to calculate load current and voltage with Thevenin\u2019s Theorem <\/h2>\n\n\n<p><span style=\"font-weight: 400;\">There are a variety of methods available to analyze complex electrical circuits<\/span>. These include <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mesh_analysis\"><span style=\"font-weight: 400;\">Mesh Analysis<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Nodal_analysis\"><span style=\"font-weight: 400;\">Nodal Analysis<\/span><\/a><span style=\"font-weight: 400;\">, or <\/span><a href=\"https:\/\/www.autodesk.com\/products\/eagle\/blog\/kirchhoffs-law-for-complex-circuits\/\"><span style=\"font-weight: 400;\">Kirchhoff&#8217;s Circuit Laws<\/span><\/a><span style=\"font-weight: 400;\">. The problem is when you\u2019re designing a DC power network,<\/span> you\u2019ll have a load whose value will change as your design process unfolds. Rather than having to recalculate the current and voltage of your entire circuit each time your load changes, you can simplify this process with Thevenin\u2019s Theorem. This blog will look at simplifying<span style=\"font-weight: 400;\"> any complex linear circuit into a single voltage source and series resistance. From there, we can use our Thevenin equivalent circuit to calculate our current and voltage quickly. Let\u2019s get started.<\/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\/free-trial?mktvar004=4333583042&#038;internalc=true\" class=\"cta-button white-button\">Get a 30-Day Free Trial<\/a>\n            <a href=\"https:\/\/www.autodesk.com\/campaigns\/fusion-360\/pricing.mobile?term=1-YEAR&#038;tab=subscription&#038;plc=FSN&#038;mktvar004=4333583043&#038;internalc=true\" 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\n<h2 class=\"wp-block-heading\" id=\"what-is-thevenins-theorem\">What is Thevenin\u2019s Theorem?<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">Like all other mathematical and scientific theories\/laws, Thevenin\u2019s Theorem was invented by the man himself, <\/span><a href=\"https:\/\/www.revolvy.com\/main\/index.php?s=L%C3%A9on%20Charles%20Th%C3%A9venin&amp;item_type=topic\"><span style=\"font-weight: 400;\">L\u00e9on Charles Th\u00e9venin<\/span><\/a>. <span style=\"font-weight: 400;\">Th\u00e9venin<\/span> was<span style=\"font-weight: 400;\"> a French telegraph engineer born in Meaux, France. After his time in the corps of telegraph engineers, <\/span>he<span style=\"font-weight: 400;\"> was appointed as a teaching inspector at the <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/T%C3%A9l%C3%A9com_ParisTech\"><span style=\"font-weight: 400;\">\u00c9cole sup\u00e9rieure de t\u00e9l\u00e9graphie<\/span><\/a><span style=\"font-weight: 400;\"> in 1882. It was here that he became interested in the measurement of electrical circuits. A<\/span>t that time, he used the two<span style=\"font-weight: 400;\"> available methods &#8211; Kirchhoff\u2019s Circuit Laws and <a href=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/easy-running-understanding-voltage-current-resistance-ohms-law\/\">Ohm\u2019s Law<\/a>.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In an attempt to make complex circuit analysis easier for every engineer, Thevenin developed his now famous Thevenin Theorem.<\/span> <span style=\"font-weight: 400;\">This theorem reduces complex circuits into simplified Thevenin equivalent circuits.<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong><span style=\"font-weight: 400;\">Thevenin&#8217;s Theorem states that you can take any linear circuit, which can contain several emfs and restrictive components, and simplify the circuit into one voltage source adn series resistance connected to a load. <\/span><\/strong><\/p>\n<\/blockquote>\n\n\n<h2 class=\"wp-block-heading\" id=\"why-use-thevenins-theorem\">Why use Thevenin\u2019s Theorem?<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">In this case, a linear circuit is one that includes passive components like resistors, inductors, and capacitors. However, if you\u2019re working with a circuit that includes gas-discharging or semiconductor components, then you have a nonlinear circuit. This is not what Thevenin\u2019s Theorem was suited for. So why use this theorem for linear circuit analysis?<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><b>Efficiency<\/b><span style=\"font-weight: 400;\">. Thevenin\u2019s Theorem provides an easy method for analyzing power circuits, which typically have a load that changes value during the analysis process. This theorem provides an efficient way to calculate the voltage and current flowing across a load without having to recalculate your entire circuit over again. <\/span><\/li>\n\n\n\n<li><b>Focus<\/b><span style=\"font-weight: 400;\">. Thevenin\u2019s Theorem also provides an efficient way to focus your analysis on a specific portion of a circuit. This allows you to calculate the voltage and current at a specific terminal by simplifying the rest of the circuit with Thevenin\u2019s equivalent.<\/span><\/li>\n<\/ul>\n\n\n\n<p>For example, c<span style=\"font-weight: 400;\">heck out the<\/span> <span style=\"font-weight: 400;\">circuit below. Here we have resistor R2 as our load. We want to calculate the voltage and current flowing through this resistor without having to use a time-consuming analysis method like Branch Current, Mesh Current, etc. each time the value of the load resistor changes.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">To make this easy, we can use Thevenin\u2019s Theorem to remove the load resistance and voltages. We then simplify the rest of the circuit as a single voltage source and series resistance. In this simplified Thevenin Circuit, the two resistors R1 and R3, along with secondary voltage B2, are all simplified into a single voltage source and series resistance. As far as the load resistor is concerned, the simplified voltage and resistance will operate the same as our original circuit. Now we just have two simple variables to work with in our calculations. <\/span><\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"thevenins-theorem-in-action\">Thevenin\u2019s Theorem in Action<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">Let\u2019s take a look at an example circuit and calculate the current flowing through a load resistor between two terminals. The process for analyzing a DC circuit using Thevenin\u2019s Theorem requires the following steps:<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Find the Thevenin Resistance by removing all voltage sources and load resistor. <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Find the Thevenin Voltage by plugging in the voltages. <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Use the Thevenin Resistance and Voltage to find the current flowing through the load. <\/span><\/li>\n<\/ol>\n\n\n\n<p><span style=\"font-weight: 400;\">Here is the example circuit we\u2019ll be working with:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"183\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2023\/06\/dccircuits-dcp16.gif\" alt=\"\" class=\"wp-image-57567\"\/><figcaption class=\"wp-element-caption\"><em>(<a href=\"http:\/\/www.electronics-tutorials.ws\/dccircuits\/dcp_7.html\">Image source<\/a>)<\/em><\/figcaption><\/figure>\n\n\n<h3 class=\"wp-block-heading\" id=\"step-1-thevenin-resistance\">Step 1 &#8211; Thevenin Resistance<\/h3>\n\n\n<p><span style=\"font-weight: 400;\">First, we must remove the 40 Ohm load resistor connecting terminals A and B and all voltage sources. Doing this will provide an open circuit at zero volts, leaving just the two resistors wired in series.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">To calculate the total Thevenin Resistance, we can use the following process:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"114\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/Resistance.jpg\" alt=\"\" class=\"wp-image-65405\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/Resistance.jpg 616w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/Resistance-300x56.jpg 300w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>We now need to reconnect the two voltages back into the circuit, and as&nbsp;and calculate&nbsp;the current flowing around the loop:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"728\" height=\"378\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TheveninVoltage-1.jpg\" alt=\"\" class=\"wp-image-65410\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TheveninVoltage-1.jpg 728w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TheveninVoltage-1-300x156.jpg 300w\" sizes=\"auto, (max-width: 728px) 100vw, 728px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"612\" height=\"126\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/CurrentCalculation.jpg\" alt=\"\" class=\"wp-image-65416\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/CurrentCalculation.jpg 612w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/CurrentCalculation-300x62.jpg 300w\" sizes=\"auto, (max-width: 612px) 100vw, 612px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"step-2-thevenin-voltages\">Step 2 &#8211; Thevenin Voltages<\/h3>\n\n\n<p>This current of 0.33 amperes (330mA) is common to both resistors, so the voltage drop across the&nbsp;20\u03a9&nbsp;resistor or the&nbsp;10\u03a9&nbsp;resistor can be calculated as:<\/p>\n\n\n\n<p>(<strong>V<sub>Th<\/sub>=V<sub>oc<\/sub>=V<sub>ab<\/sub><\/strong>)<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"> Our current to calculate the voltage drop, which is:<\/span><\/p>\n\n\n\n<p><strong>V<sub>AB<\/sub>&nbsp;&nbsp;=&nbsp;&nbsp;20&nbsp;&nbsp;\u2013&nbsp;&nbsp;(20\u03a9&nbsp;x&nbsp;0.33amps)&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;13.33&nbsp;volts<\/strong><\/p>\n\n\n\n<p>                                           or<\/p>\n\n\n\n<p><strong>V<sub>AB<\/sub>&nbsp;&nbsp;=&nbsp;&nbsp;10&nbsp;&nbsp;+&nbsp;&nbsp;(10\u03a9&nbsp;x&nbsp;0.33amps)&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;13.33&nbsp;volts, the same.<\/strong><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"step-3-load-current\">Step 3 &#8211; Load Current<\/h3>\n\n\n<p><span style=\"font-weight: 400;\">Now that we have our Thevenin Resistance and Voltage we can put our Thevenin equivalent circuit together with our original load resistor as shown below.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"400\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/equivalent.jpg\" alt=\"\" class=\"wp-image-65421\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/equivalent.jpg 596w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/equivalent-300x201.jpg 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">From here, we can use Ohm\u2019s Law to calculate the total current flowing across the load resistor like this:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"702\" height=\"100\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TotalCurrent_Equivalent.jpg\" alt=\"\" class=\"wp-image-65426\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TotalCurrent_Equivalent.jpg 702w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TotalCurrent_Equivalent-300x43.jpg 300w\" sizes=\"auto, (max-width: 702px) 100vw, 702px\" \/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Ready to put your skills to the test? Use Thevenin\u2019s Theorem to find the R<sub>TH<\/sub> resistance and V<sub>TH<\/sub> load for the circuit below!<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"830\" height=\"424\" src=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TestCircuit_Final.png\" alt=\"\" class=\"wp-image-65442\" srcset=\"https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TestCircuit_Final.png 830w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TestCircuit_Final-300x153.png 300w, https:\/\/www.autodesk.com\/products\/fusion-360\/blog\/wp-content\/uploads\/2024\/02\/TestCircuit_Final-768x392.png 768w\" sizes=\"auto, (max-width: 830px) 100vw, 830px\" \/><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Remember the three-step process:<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Find the Thevenin Resistance by removing all voltage sources and load. <\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Find the Thevenin Voltage by reconnecting the voltage sources.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Use the Thevenin Resistance and Voltage to find the total current flowing through the load.<\/span><\/li>\n<\/ol>\n\n\n<h2 class=\"wp-block-heading\" id=\"keep-it-simple\">Keep it simple<\/h2>\n\n\n<p><span style=\"font-weight: 400;\">Planning to design a DC power circuit? Chances are you\u2019ll be incorporating a load whose value will change during your circuit analysis. Rather than having to recalculate the entire circuit each time you change the value of this load, you now have Thevenin\u2019s Theorem to make your job easy.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">This theorem allows you to take any complex linear circuit with a variety of resistive components and EMFs and simplify it into a Thevenin equivalent circuit. With this simplified circuit, you can easily calculate the total current and voltage flowing through a load. This is a huge time saver for any engineer who needs to analyze circuits for power designs and other complex applications efficiently.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">For those of you visual\/kinesthetic learners, be sure to check out the video below that shows how to use Thevenin\u2019s Theorem step-by-step.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Ready to design your first power circuit? <\/span>Try Autodesk <a href=\"https:\/\/www.autodesk.com\/solutions\/electronics-design-software\">Fusion 360 electronics<\/a> for free today!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Learn how to use Thevenin\u2019s Theorem to calculate current and voltage across a load resistor in a linear circuit.<\/p>\n","protected":false},"author":3911,"featured_media":33962,"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":[209,207],"coauthors":[589],"class_list":["post-1633","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics-engineering","tag-electrical-engineer","tag-electronics","dhig-theme--light"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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