{"id":179654,"date":"2025-01-02T04:19:18","date_gmt":"2025-01-02T04:19:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179654"},"modified":"2025-01-02T04:19:20","modified_gmt":"2025-01-02T04:19:20","slug":"a-45-mh-ideal-inductor-is-connected-in-series-with-a-60-q-resistor-through-an-ideal-15-v-dc-power-supply-and-an-open-switch","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/02\/a-45-mh-ideal-inductor-is-connected-in-series-with-a-60-q-resistor-through-an-ideal-15-v-dc-power-supply-and-an-open-switch\/","title":{"rendered":"A 45-mH ideal inductor is connected in series with a 60-Q resistor through an ideal 15-V DC power supply and an open switch"},"content":{"rendered":"\n<p>A 45-mH ideal inductor is connected in series with a 60-Q resistor through an ideal 15-V DC power supply and an open switch. If the switch is closed at time t = 0 s, what is the current 7 ms later? <\/p>\n\n\n\n<p>250 mA <\/p>\n\n\n\n<p>650 mA <\/p>\n\n\n\n<p>500 mA <\/p>\n\n\n\n<p>800 mA<\/p>\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 solve for the current in the circuit 7 ms after closing the switch, we need to analyze the behavior of the RL circuit. The equation governing the current in an RL circuit is:<\/p>\n\n\n\n<p>[<br>I(t) = \\frac{V}{R} \\left( 1 &#8211; e^{-\\frac{R}{L} t} \\right)<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( I(t) ) is the current at time ( t ),<\/li>\n\n\n\n<li>( V ) is the voltage of the power supply (15 V),<\/li>\n\n\n\n<li>( R ) is the resistance (60 \u03a9),<\/li>\n\n\n\n<li>( L ) is the inductance (45 mH = 0.045 H),<\/li>\n\n\n\n<li>( t ) is the time (7 ms = 0.007 s).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the time constant<\/h3>\n\n\n\n<p>The time constant ( \\tau ) of an RL circuit is given by:<\/p>\n\n\n\n<p>[<br>\\tau = \\frac{L}{R}<br>]<\/p>\n\n\n\n<p>Substituting the given values:<\/p>\n\n\n\n<p>[<br>\\tau = \\frac{0.045}{60} = 0.00075 \\, \\text{s} \\, (0.75 \\, \\text{ms})<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the formula for current<\/h3>\n\n\n\n<p>Now, we can calculate the current at ( t = 7 \\, \\text{ms} ) (which is 0.007 s) using the equation for current in an RL circuit:<\/p>\n\n\n\n<p>[<br>I(t) = \\frac{V}{R} \\left( 1 &#8211; e^{-\\frac{R}{L} t} \\right)<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>I(0.007) = \\frac{15}{60} \\left( 1 &#8211; e^{-\\frac{60}{0.045} \\times 0.007} \\right)<br>]<\/p>\n\n\n\n<p>First, calculate the exponent:<\/p>\n\n\n\n<p>[<br>\\frac{60}{0.045} = 1333.33, \\quad 1333.33 \\times 0.007 = 9.3333<br>]<\/p>\n\n\n\n<p>So,<\/p>\n\n\n\n<p>[<br>I(0.007) = 0.25 \\left( 1 &#8211; e^{-9.3333} \\right)<br>]<\/p>\n\n\n\n<p>Since ( e^{-9.3333} ) is a very small value close to 0, the expression simplifies to:<\/p>\n\n\n\n<p>[<br>I(0.007) \\approx 0.25 \\times (1 &#8211; 0) = 0.25 \\, \\text{A} = 250 \\, \\text{mA}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The current 7 ms after the switch is closed is <strong>250 mA<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 45-mH ideal inductor is connected in series with a 60-Q resistor through an ideal 15-V DC power supply and an open switch. If the switch is closed at time t = 0 s, what is the current 7 ms later? 250 mA 650 mA 500 mA 800 mA The Correct Answer and Explanation is [&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-179654","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179654","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=179654"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179654\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}