{"id":195582,"date":"2025-02-28T13:11:26","date_gmt":"2025-02-28T13:11:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195582"},"modified":"2025-02-28T13:11:29","modified_gmt":"2025-02-28T13:11:29","slug":"10-0-resistor-and-a-40-0-resistor-in-series-are-connected-to-a-120-v-dc-source","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/10-0-resistor-and-a-40-0-resistor-in-series-are-connected-to-a-120-v-dc-source\/","title":{"rendered":"10.0- resistor and a 40.0- resistor in series are connected to a 120-V dc source"},"content":{"rendered":"\n<p>10.0- resistor and a 40.0- resistor in series are connected to a 120-V dc source. (a) What is (are) the current(s) through the resistors current through the 10.0- resistor: A current through the 40.0- resistor: A (b) What is the voltage drop across each resistor voltage drop across the 10.0- resistor: V voltage drop across the 40.0-? resistor: V<\/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>In a series circuit, the current flowing through each resistor is the same, while the voltage drop across each resistor depends on its resistance. Given a 10.0\u202f\u03a9 resistor and a 40.0\u202f\u03a9 resistor connected in series to a 120\u202fV DC source, we can determine the current through the resistors and the voltage drop across each.<\/p>\n\n\n\n<p><strong>(a) Current through the resistors:<\/strong><\/p>\n\n\n\n<p>The total resistance ( R_{\\text{total}} ) in a series circuit is the sum of the individual resistances:<\/p>\n\n\n\n<p>[ R_{\\text{total}} = R_1 + R_2 = 10.0\\, \\Omega + 40.0\\, \\Omega = 50.0\\, \\Omega ]<\/p>\n\n\n\n<p>Using Ohm&#8217;s Law, ( V = I \\times R ), we can solve for the current ( I ):<\/p>\n\n\n\n<p>[ I = \\frac{V}{R_{\\text{total}}} = \\frac{120\\, \\text{V}}{50.0\\, \\Omega} = 2.4\\, \\text{A} ]<\/p>\n\n\n\n<p>Therefore, the current through both the 10.0\u202f\u03a9 and 40.0\u202f\u03a9 resistors is 2.4\u202fA.<\/p>\n\n\n\n<p><strong>(b) Voltage drop across each resistor:<\/strong><\/p>\n\n\n\n<p>The voltage drop ( V ) across a resistor in a series circuit can be calculated using Ohm&#8217;s Law: ( V = I \\times R ).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Voltage drop across the 10.0\u202f\u03a9 resistor:<\/strong> [ V_{10} = I \\times R_1 = 2.4\\, \\text{A} \\times 10.0\\, \\Omega = 24.0\\, \\text{V} ]<\/li>\n\n\n\n<li><strong>Voltage drop across the 40.0\u202f\u03a9 resistor:<\/strong> [ V_{40} = I \\times R_2 = 2.4\\, \\text{A} \\times 40.0\\, \\Omega = 96.0\\, \\text{V} ]<\/li>\n<\/ul>\n\n\n\n<p>These voltage drops add up to the total supplied voltage:<\/p>\n\n\n\n<p>[ V_{10} + V_{40} = 24.0\\, \\text{V} + 96.0\\, \\text{V} = 120.0\\, \\text{V} ]<\/p>\n\n\n\n<p>This confirms that the calculations are consistent with the total voltage of the source.<\/p>\n\n\n\n<p>In summary, when resistors are connected in series, the same current flows through each resistor, and the voltage drop across each resistor is proportional to its resistance. In this case, a 2.4\u202fA current flows through both the 10.0\u202f\u03a9 and 40.0\u202f\u03a9 resistors, resulting in voltage drops of 24.0\u202fV and 96.0\u202fV, respectively.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.imgur.com\/3g1rY8f.png\" alt=\"Series Circuit Diagram\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>10.0- resistor and a 40.0- resistor in series are connected to a 120-V dc source. (a) What is (are) the current(s) through the resistors current through the 10.0- resistor: A current through the 40.0- resistor: A (b) What is the voltage drop across each resistor voltage drop across the 10.0- resistor: V voltage drop across [&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-195582","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195582","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=195582"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195582\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}