{"id":185587,"date":"2025-01-22T18:20:32","date_gmt":"2025-01-22T18:20:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185587"},"modified":"2025-01-22T18:20:34","modified_gmt":"2025-01-22T18:20:34","slug":"determine-the-current-through-each-resistor","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/determine-the-current-through-each-resistor\/","title":{"rendered":"Determine the current through each resistor"},"content":{"rendered":"\n<p>Determine the current through each resistor in Figure 75; then calculate each voltage drop.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-404.png\" alt=\"\" class=\"wp-image-185589\"\/><\/figure>\n\n\n\n<p>Determine the current through each resistor in both circuits of Figure 76; then calculate each voltage drop.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-405.png\" alt=\"\" class=\"wp-image-185590\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>I&#8217;m unable to view the specific figures you&#8217;ve referenced, but I can guide you through the general process of analyzing resistive circuits to determine the current through each resistor and calculate the voltage drops. Here&#8217;s a step-by-step approach:<\/p>\n\n\n\n<p><strong>1. Identify Series and Parallel Components:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Series Connection:<\/strong> Resistors are in series if the same current flows through them. The total resistance is the sum of individual resistances:<br>[ R_{\\text{total}} = R_1 + R_2 + \\dots + R_n ]<\/li>\n\n\n\n<li><strong>Parallel Connection:<\/strong> Resistors are in parallel if they share the same voltage across them. The total resistance is given by:<br>[ \\frac{1}{R_{\\text{total}}} = \\frac{1}{R_1} + \\frac{1}{R_2} + \\dots + \\frac{1}{R_n} ]<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Simplify the Circuit:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Combine series and parallel resistors step by step to reduce the circuit to a single equivalent resistance.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. Apply Ohm&#8217;s Law:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Once you have the total resistance, use Ohm&#8217;s Law to find the total current supplied by the source:<br>[ I_{\\text{total}} = \\frac{V_{\\text{source}}}{R_{\\text{total}}} ]<\/li>\n<\/ul>\n\n\n\n<p><strong>4. Determine Individual Currents:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>For Series Circuits:<\/strong> The current is the same through all resistors.<\/li>\n\n\n\n<li><strong>For Parallel Circuits:<\/strong> Use the current division rule to find the current through each resistor:<br>[ I_n = I_{\\text{total}} \\times \\frac{R_{\\text{total}}}{R_n} ]<\/li>\n<\/ul>\n\n\n\n<p><strong>5. Calculate Voltage Drops:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use Ohm&#8217;s Law to find the voltage drop across each resistor:<br>[ V_n = I_n \\times R_n ]<\/li>\n<\/ul>\n\n\n\n<p><strong>Example:<\/strong><br>Consider a circuit with a 12V battery connected to three resistors: R\u2081 = 2\u03a9, R\u2082 = 3\u03a9, and R\u2083 = 6\u03a9. If R\u2082 and R\u2083 are in parallel, and their combination is in series with R\u2081:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Combine R\u2082 and R\u2083 in Parallel:<\/strong><br>[ \\frac{1}{R_{\\text{23}}} = \\frac{1}{3} + \\frac{1}{6} = \\frac{1}{2} \\quad \\Rightarrow \\quad R_{\\text{23}} = 2\u03a9 ]<\/li>\n\n\n\n<li><strong>Total Resistance:<\/strong><br>[ R_{\\text{total}} = R_1 + R_{\\text{23}} = 2\u03a9 + 2\u03a9 = 4\u03a9 ]<\/li>\n\n\n\n<li><strong>Total Current:<\/strong><br>[ I_{\\text{total}} = \\frac{12V}{4\u03a9} = 3A ]<\/li>\n\n\n\n<li><strong>Current Through R\u2082 and R\u2083:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since R\u2082 and R\u2083 are in parallel, the voltage across them is the same.<\/li>\n\n\n\n<li>The current through R\u2082:<br>[ I_2 = I_{\\text{total}} \\times \\frac{R_{\\text{23}}}{R_2} = 3A \\times \\frac{2\u03a9}{3\u03a9} = 2A ]<\/li>\n\n\n\n<li>The current through R\u2083:<br>[ I_3 = I_{\\text{total}} \\times \\frac{R_{\\text{23}}}{R_3} = 3A \\times \\frac{2\u03a9}{6\u03a9} = 1A ]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Voltage Drops:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Across R\u2081:<br>[ V_1 = I_{\\text{total}} \\times R_1 = 3A \\times 2\u03a9 = 6V ]<\/li>\n\n\n\n<li>Across R\u2082:<br>[ V_2 = I_2 \\times R_2 = 2A \\times 3\u03a9 = 6V ]<\/li>\n\n\n\n<li>Across R\u2083:<br>[ V_3 = I_3 \\times R_3 = 1A \\times 6\u03a9 = 6V ]<\/li>\n<\/ul>\n\n\n\n<p>This example illustrates how to analyze a resistive circuit to determine currents and voltage drops. By systematically applying these steps, you can solve similar problems involving different resistor configurations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine the current through each resistor in Figure 75; then calculate each voltage drop. Determine the current through each resistor in both circuits of Figure 76; then calculate each voltage drop. The Correct Answer and Explanation is : I&#8217;m unable to view the specific figures you&#8217;ve referenced, but I can guide you through the general [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-185587","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185587","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=185587"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185587\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}