{"id":189614,"date":"2025-02-10T05:51:23","date_gmt":"2025-02-10T05:51:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189614"},"modified":"2025-02-10T05:51:25","modified_gmt":"2025-02-10T05:51:25","slug":"a-10-%cf%89-resistor-dissipates-1-w-of-power-when-connected-to-a-dc-voltage-source","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/10\/a-10-%cf%89-resistor-dissipates-1-w-of-power-when-connected-to-a-dc-voltage-source\/","title":{"rendered":"A 10-\u03a9 resistor dissipates 1 W of power when connected to a dc voltage source"},"content":{"rendered":"\n<p>A 10-\u03a9 resistor dissipates 1 W of power when connected to a dc voltage source. If the value of dc voltage is doubled, the resistor will dissipate<\/p>\n\n\n\n<p>a. 1 W.<\/p>\n\n\n\n<p>b. 2 W.<\/p>\n\n\n\n<p>c. 4 W.<\/p>\n\n\n\n<p>d. 10 W<\/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>c. 4 W<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To solve this, we can use the relationship between power (( P )), voltage (( V )), and resistance (( R )), which is given by the formula:<\/p>\n\n\n\n<p>[<br>P = \\frac{V^2}{R}<br>]<\/p>\n\n\n\n<p>We are told that a 10-\u03a9 resistor dissipates 1 W of power when connected to a DC voltage source. Using this formula, we can first calculate the voltage applied across the resistor when it dissipates 1 W of power.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the voltage when the power is 1 W.<\/h3>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( P = 1 \\, \\text{W} )<\/li>\n\n\n\n<li>( R = 10 \\, \\Omega )<\/li>\n<\/ul>\n\n\n\n<p>Substitute the known values into the formula:<\/p>\n\n\n\n<p>[<br>1 = \\frac{V^2}{10}<br>]<\/p>\n\n\n\n<p>Solving for ( V^2 ):<\/p>\n\n\n\n<p>[<br>V^2 = 1 \\times 10 = 10<br>]<\/p>\n\n\n\n<p>[<br>V = \\sqrt{10} \\approx 3.16 \\, \\text{V}<br>]<\/p>\n\n\n\n<p>So, the initial voltage across the resistor is approximately 3.16 V.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Double the voltage.<\/h3>\n\n\n\n<p>Now, if the voltage is doubled, the new voltage becomes:<\/p>\n\n\n\n<p>[<br>V_{\\text{new}} = 2 \\times 3.16 = 6.32 \\, \\text{V}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the new power dissipation.<\/h3>\n\n\n\n<p>The power dissipated by the resistor when the voltage is increased can be calculated using the same formula:<\/p>\n\n\n\n<p>[<br>P_{\\text{new}} = \\frac{V_{\\text{new}}^2}{R}<br>]<\/p>\n\n\n\n<p>Substitute ( V_{\\text{new}} = 6.32 \\, \\text{V} ) and ( R = 10 \\, \\Omega ):<\/p>\n\n\n\n<p>[<br>P_{\\text{new}} = \\frac{6.32^2}{10} = \\frac{39.94}{10} \\approx 4 \\, \\text{W}<br>]<\/p>\n\n\n\n<p>Thus, when the voltage is doubled, the power dissipated by the resistor increases to approximately 4 W. This result is consistent with the relationship that power dissipated in a resistor is proportional to the square of the applied voltage. Therefore, doubling the voltage causes the power to increase by a factor of four.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 10-\u03a9 resistor dissipates 1 W of power when connected to a dc voltage source. If the value of dc voltage is doubled, the resistor will dissipate a. 1 W. b. 2 W. c. 4 W. d. 10 W The Correct Answer and Explanation is : The correct answer is c. 4 W. Explanation: To [&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-189614","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189614","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=189614"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189614\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189614"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189614"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}