{"id":86305,"date":"2025-06-01T03:43:01","date_gmt":"2025-06-01T03:43:01","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=86305"},"modified":"2025-06-01T03:43:01","modified_gmt":"2025-06-01T03:43:01","slug":"a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/","title":{"rendered":"A metal wire of length l and diameter d has a resistance R. What would"},"content":{"rendered":"

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ?<\/p>\n

[amp_mcq option1=”R” option2=”R\/4″ option3=”R\/2″ option4=”2R” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-2 – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2).
\nIf the diameter is doubled (2d), the new area becomes A’ = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A’ = 4A).
\nSince R \u221d 1\/A, the new resistance R’ will be R’ = R \/ (A’\/A) = R \/ 4.
\n<\/section>\n
\n– Resistance is inversely proportional to the cross-sectional area of the wire.
\n– Cross-sectional area is proportional to the square of the diameter.
\n<\/section>\n
\nThe resistivity (\u03c1) depends on the material of the wire, which is stated as the same in the question. The length (L) is also stated as the same. Therefore, only the change in diameter affects the resistance in this case.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ? [amp_mcq option1=”R” option2=”R\/4″ option3=”R\/2″ option4=”2R” correct=”option2″] This question was previously asked in UPSC CDS-2 – 2022 Download PDFAttempt Online The … <\/p>\n

Detailed SolutionA metal wire of length l and diameter d has a resistance R. What would<\/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":[1088],"tags":[1108,1200,1128],"class_list":["post-86305","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-2","tag-1108","tag-conductivity","tag-physics","no-featured-image-padding"],"yoast_head":"\nA metal wire of length l and diameter d has a resistance R. What would<\/title>\n<meta name=\"description\" content=\"The resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2). If the diameter is doubled (2d), the new area becomes A' = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A' = 4A). Since R \u221d 1\/A, the new resistance R' will be R' = R \/ (A'\/A) = R \/ 4. - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.\" \/>\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\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A metal wire of length l and diameter d has a resistance R. What would\" \/>\n<meta property=\"og:description\" content=\"The resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2). If the diameter is doubled (2d), the new area becomes A' = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A' = 4A). Since R \u221d 1\/A, the new resistance R' will be R' = R \/ (A'\/A) = R \/ 4. - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T03:43:01+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":"A metal wire of length l and diameter d has a resistance R. What would","description":"The resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2). If the diameter is doubled (2d), the new area becomes A' = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A' = 4A). Since R \u221d 1\/A, the new resistance R' will be R' = R \/ (A'\/A) = R \/ 4. - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.","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\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/","og_locale":"en_US","og_type":"article","og_title":"A metal wire of length l and diameter d has a resistance R. What would","og_description":"The resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2). If the diameter is doubled (2d), the new area becomes A' = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A' = 4A). Since R \u221d 1\/A, the new resistance R' will be R' = R \/ (A'\/A) = R \/ 4. - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T03:43:01+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\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/","name":"A metal wire of length l and diameter d has a resistance R. What would","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T03:43:01+00:00","dateModified":"2025-06-01T03:43:01+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The resistance (R) of a wire is given by the formula R = \u03c1(L\/A), where \u03c1 is the resistivity of the material, L is the length, and A is the cross-sectional area. The area A of a circular wire is given by A = \u03c0(d\/2)^2 = \u03c0d^2\/4, where d is the diameter. So, R is inversely proportional to the square of the diameter (R \u221d 1\/d^2). If the diameter is doubled (2d), the new area becomes A' = \u03c0(2d)^2\/4 = \u03c0(4d^2)\/4 = \u03c0d^2. This means the area becomes four times the original area (A' = 4A). Since R \u221d 1\/A, the new resistance R' will be R' = R \/ (A'\/A) = R \/ 4. - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-metal-wire-of-length-l-and-diameter-d-has-a-resistance-r-what-would\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-2\/"},{"@type":"ListItem","position":3,"name":"A metal wire of length l and diameter d has a resistance R. 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