{"id":185145,"date":"2025-01-22T07:03:38","date_gmt":"2025-01-22T07:03:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185145"},"modified":"2025-01-22T07:03:54","modified_gmt":"2025-01-22T07:03:54","slug":"find-i1-and-vo-in-the-network-infigure","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/find-i1-and-vo-in-the-network-infigure\/","title":{"rendered":"Find I1 and Vo in the network in figure"},"content":{"rendered":"\n<p>Find I1 and Vo in the network infigure.<\/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-388.png\" alt=\"\" class=\"wp-image-185146\"\/><\/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>To determine the current ( I_1 ) and the output voltage ( V_o ) in the given circuit, we can employ the mesh-current analysis method. This technique involves defining mesh currents for each independent loop in the circuit and applying Kirchhoff&#8217;s Voltage Law (KVL) to establish equations that describe the voltage drops around each loop.<\/p>\n\n\n\n<p><strong>Step 1: Define Mesh Currents<\/strong><\/p>\n\n\n\n<p>Assume the circuit consists of two loops:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mesh 1<\/strong>: Loop containing the 10 V voltage source, resistor ( R_1 ), and resistor ( R_2 ).<\/li>\n\n\n\n<li><strong>Mesh 2<\/strong>: Loop containing resistor ( R_2 ), resistor ( R_3 ), and the dependent current source ( 2I_1 ).<\/li>\n<\/ul>\n\n\n\n<p>Let ( I_1 ) be the mesh current for Mesh 1 and ( I_2 ) for Mesh 2.<\/p>\n\n\n\n<p><strong>Step 2: Apply KVL to Each Mesh<\/strong><\/p>\n\n\n\n<p>For <strong>Mesh 1<\/strong>:<\/p>\n\n\n\n<p>Starting from the 10 V source and moving clockwise:<\/p>\n\n\n\n<p>[ 10 V &#8211; I_1 R_1 &#8211; (I_1 &#8211; I_2) R_2 = 0 ]<\/p>\n\n\n\n<p>Simplifying:<\/p>\n\n\n\n<p>[ 10 = I_1 (R_1 + R_2) &#8211; I_2 R_2 ]<\/p>\n\n\n\n<p>For <strong>Mesh 2<\/strong>:<\/p>\n\n\n\n<p>Considering the dependent current source ( 2I_1 ), the current ( I_2 ) is equal to ( 2I_1 ).<\/p>\n\n\n\n<p>Therefore:<\/p>\n\n\n\n<p>[ I_2 = 2I_1 ]<\/p>\n\n\n\n<p><strong>Step 3: Solve the Equations<\/strong><\/p>\n\n\n\n<p>Substitute ( I_2 = 2I_1 ) into the equation from Mesh 1:<\/p>\n\n\n\n<p>[ 10 = I_1 (R_1 + R_2) &#8211; 2I_1 R_2 ]<\/p>\n\n\n\n<p>Simplify:<\/p>\n\n\n\n<p>[ 10 = I_1 (R_1 + R_2 &#8211; 2R_2) ]<\/p>\n\n\n\n<p>[ 10 = I_1 (R_1 &#8211; R_2) ]<\/p>\n\n\n\n<p>Solve for ( I_1 ):<\/p>\n\n\n\n<p>[ I_1 = \\frac{10}{R_1 &#8211; R_2} ]<\/p>\n\n\n\n<p>Given ( I_2 = 2I_1 ):<\/p>\n\n\n\n<p>[ I_2 = \\frac{20}{R_1 &#8211; R_2} ]<\/p>\n\n\n\n<p><strong>Step 4: Determine ( V_o )<\/strong><\/p>\n\n\n\n<p>The output voltage ( V_o ) is the voltage across resistor ( R_3 ):<\/p>\n\n\n\n<p>[ V_o = I_2 \\times R_3 ]<\/p>\n\n\n\n<p>Substitute ( I_2 ):<\/p>\n\n\n\n<p>[ V_o = \\frac{20 \\times R_3}{R_1 &#8211; R_2} ]<\/p>\n\n\n\n<p><strong>Conclusion<\/strong><\/p>\n\n\n\n<p>By applying mesh-current analysis, we&#8217;ve expressed ( I_1 ) and ( V_o ) in terms of the resistances ( R_1 ), ( R_2 ), and ( R_3 ). To obtain numerical values, specific resistance values are required. This methodical approach ensures a systematic solution to circuit analysis problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find I1 and Vo in the network infigure. The Correct Answer and Explanation is : To determine the current ( I_1 ) and the output voltage ( V_o ) in the given circuit, we can employ the mesh-current analysis method. This technique involves defining mesh currents for each independent loop in the circuit and applying [&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-185145","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185145","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=185145"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}