{"id":84630,"date":"2025-06-01T02:42:07","date_gmt":"2025-06-01T02:42:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=84630"},"modified":"2025-06-01T02:42:07","modified_gmt":"2025-06-01T02:42:07","slug":"suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/","title":{"rendered":"Suppose voltage V is applied across a resistance R. The power dissipat"},"content":{"rendered":"

Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be<\/p>\n

[amp_mcq option1=”P” option2=”3P” option3=”P\/3″ option4=”2P\/3″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-1 – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is B) 3P.
\n<\/section>\n
\nIn the first case, power dissipated is P = V\u00b2\/R.
\nIn the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3.
\nThe power dissipated in the second case is P’ = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P’ = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R).
\nSince P = V\u00b2\/R, the power dissipated in the second case is P’ = 3P.
\n<\/section>\n
\nWhen resistors are connected in parallel across a constant voltage source, the total power dissipated is the sum of the power dissipated in each resistor. In this case, each of the three resistors R has voltage V across it, so each dissipates power P = V\u00b2\/R. The total power is P + P + P = 3P. Using the equivalent resistance method confirms this result.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be [amp_mcq option1=”P” option2=”3P” option3=”P\/3″ option4=”2P\/3″ correct=”option2″] This question was … <\/p>\n

Detailed SolutionSuppose voltage V is applied across a resistance R. The power dissipat<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1087],"tags":[1101,1201,1128],"class_list":["post-84630","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-1","tag-1101","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nSuppose voltage V is applied across a resistance R. The power dissipat<\/title>\n<meta name=\"description\" content=\"The correct answer is B) 3P. In the first case, power dissipated is P = V\u00b2\/R. In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3. The power dissipated in the second case is P' = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P' = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R). Since P = V\u00b2\/R, the power dissipated in the second case is P' = 3P.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose voltage V is applied across a resistance R. The power dissipat\" \/>\n<meta property=\"og:description\" content=\"The correct answer is B) 3P. In the first case, power dissipated is P = V\u00b2\/R. In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3. The power dissipated in the second case is P' = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P' = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R). Since P = V\u00b2\/R, the power dissipated in the second case is P' = 3P.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T02:42:07+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Suppose voltage V is applied across a resistance R. The power dissipat","description":"The correct answer is B) 3P. In the first case, power dissipated is P = V\u00b2\/R. In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3. The power dissipated in the second case is P' = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P' = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R). Since P = V\u00b2\/R, the power dissipated in the second case is P' = 3P.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/","og_locale":"en_US","og_type":"article","og_title":"Suppose voltage V is applied across a resistance R. The power dissipat","og_description":"The correct answer is B) 3P. In the first case, power dissipated is P = V\u00b2\/R. In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3. The power dissipated in the second case is P' = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P' = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R). Since P = V\u00b2\/R, the power dissipated in the second case is P' = 3P.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T02:42:07+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/","name":"Suppose voltage V is applied across a resistance R. The power dissipat","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T02:42:07+00:00","dateModified":"2025-06-01T02:42:07+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is B) 3P. In the first case, power dissipated is P = V\u00b2\/R. In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 \/ (1\/R + 1\/R + 1\/R) = 1 \/ (3\/R) = R\/3. The power dissipated in the second case is P' = V\u00b2\/R_eq. Substituting R_eq = R\/3, we get P' = V\u00b2\/(R\/3) = 3 * (V\u00b2\/R). Since P = V\u00b2\/R, the power dissipated in the second case is P' = 3P.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-voltage-v-is-applied-across-a-resistance-r-the-power-dissipat\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-1","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-1\/"},{"@type":"ListItem","position":3,"name":"Suppose voltage V is applied across a resistance R. 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