{"id":150002,"date":"2024-10-08T08:52:53","date_gmt":"2024-10-08T08:52:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=150002"},"modified":"2024-10-08T08:52:56","modified_gmt":"2024-10-08T08:52:56","slug":"how-long-will-it-take-for-a-50-%c2%b5f-capacitor-to-fully-charge-if-it-is-in-a-series-circuit-with-a-100-k%cf%89-resistor","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/08\/how-long-will-it-take-for-a-50-%c2%b5f-capacitor-to-fully-charge-if-it-is-in-a-series-circuit-with-a-100-k%cf%89-resistor\/","title":{"rendered":"How long will it take for a 50 \u00b5F capacitor to fully charge if it is in a series circuit with a 100 K\u03a9 resistor"},"content":{"rendered":"\n<p>How long will it take for a 50 \u00b5F capacitor to fully charge if it is in a series circuit with a 100 K\u03a9 resistor?<\/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>The correct answer is:  <strong>25 seconds<\/strong><\/p>\n\n\n\n<p>To determine how long it will take for a 50 \u00b5F capacitor to fully charge in a series circuit with a 100 k\u03a9 resistor, we can use the time constant formula of an RC (resistor-capacitor) circuit. The time constant (( \\tau )) is given by:<\/p>\n\n\n\n<p>[<br>\\tau = R \\times C<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\tau ) is the time constant in seconds,<\/li>\n\n\n\n<li>( R ) is the resistance in ohms,<\/li>\n\n\n\n<li>( C ) is the capacitance in farads.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( R = 100,000 \\, \\Omega ) (100 k\u03a9)<\/li>\n\n\n\n<li>( C = 50 \\, \\mu F = 50 \\times 10^{-6} \\, F )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation of the Time Constant:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Convert capacitance to farads:<br>[<br>C = 50 \\times 10^{-6} \\, F<br>]<\/li>\n\n\n\n<li>Plug in the values:<br>[<br>\\tau = 100,000 \\, \\Omega \\times 50 \\times 10^{-6} \\, F = 5 \\, seconds<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Charging Time:<\/h3>\n\n\n\n<p>The capacitor charges approximately to 63.2% of the supply voltage after one time constant (( \\tau )). The charging curve of the capacitor can be described by the equation:<\/p>\n\n\n\n<p>[<br>V(t) = V_{max} \\left(1 &#8211; e^{-t\/\\tau}\\right)<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( V(t) ) is the voltage across the capacitor at time ( t ),<\/li>\n\n\n\n<li>( V_{max} ) is the maximum voltage (supply voltage),<\/li>\n\n\n\n<li>( e ) is the base of the natural logarithm (approximately 2.718).<\/li>\n<\/ul>\n\n\n\n<p>To consider the time it takes to &#8220;fully charge&#8221; (approaching ( V_{max} )), it&#8217;s often considered that after about ( 5\\tau ) (or 5 time constants), the capacitor will be over 99% charged.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Calculation:<\/h3>\n\n\n\n<p>For our case:<br>[<br>5 \\tau = 5 \\times 5 \\, seconds = 25 \\, seconds<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Thus, it will take approximately <strong>25 seconds<\/strong> for the 50 \u00b5F capacitor to fully charge in a series circuit with a 100 k\u03a9 resistor. This calculation assumes ideal conditions without any significant losses, allowing the capacitor to reach a near-complete charge relative to the applied voltage.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How long will it take for a 50 \u00b5F capacitor to fully charge if it is in a series circuit with a 100 K\u03a9 resistor? The Correct Answer and Explanation is : The correct answer is: 25 seconds To determine how long it will take for a 50 \u00b5F capacitor to fully charge in a [&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-150002","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150002","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=150002"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150002\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150002"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150002"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}