{"id":84649,"date":"2025-06-01T02:43:19","date_gmt":"2025-06-01T02:43:19","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=84649"},"modified":"2025-06-01T02:43:19","modified_gmt":"2025-06-01T02:43:19","slug":"a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/","title":{"rendered":"A copper wire of radius r and length 1 has a resistance of R. A second"},"content":{"rendered":"

A copper wire of radius r and length 1 has a resistance of R. A second copper wire with radius 2r and length 1 is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be<\/p>\n

[amp_mcq option1=”5R” option2=”5\/4 R” option3=”4\/5 R” option4=”R\/5″ correct=”option4″]<\/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 resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius.
\n<\/section>\n
\n– For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2).
\n– For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4.
\n– When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082).
\n– Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4).
\n– R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.
\n<\/section>\n
\nThis problem illustrates the relationship between resistance, material properties, and geometry, as well as the calculation of equivalent resistance in a parallel circuit. The resistivity (\u03c1) is the same for both wires as they are both copper.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A copper wire of radius r and length 1 has a resistance of R. A second copper wire with radius 2r and length 1 is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be [amp_mcq option1=”5R” option2=”5\/4 R” option3=”4\/5 R” … <\/p>\n

Detailed SolutionA copper wire of radius r and length 1 has a resistance of R. A second<\/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-84649","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":"\nA copper wire of radius r and length 1 has a resistance of R. A second<\/title>\n<meta name=\"description\" content=\"The resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius. - For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2). - For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4. - When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082). - Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4). - R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.\" \/>\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-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A copper wire of radius r and length 1 has a resistance of R. A second\" \/>\n<meta property=\"og:description\" content=\"The resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius. - For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2). - For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4. - When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082). - Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4). - R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T02:43:19+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 copper wire of radius r and length 1 has a resistance of R. A second","description":"The resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius. - For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2). - For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4. - When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082). - Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4). - R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.","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-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/","og_locale":"en_US","og_type":"article","og_title":"A copper wire of radius r and length 1 has a resistance of R. A second","og_description":"The resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius. - For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2). - For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4. - When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082). - Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4). - R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T02:43:19+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-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/","name":"A copper wire of radius r and length 1 has a resistance of R. A second","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T02:43:19+00:00","dateModified":"2025-06-01T02:43:19+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The resistance 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 of a circular wire is A = \u03c0r\u00b2, where r is the radius. - For the first wire: R\u2081 = R = \u03c1 * (l \/ \u03c0r\u00b2). - For the second wire: The radius is 2r, and the length is l. So, R\u2082 = \u03c1 * (l \/ \u03c0(2r)\u00b2) = \u03c1 * (l \/ 4\u03c0r\u00b2) = (1\/4) * [\u03c1 * (l \/ \u03c0r\u00b2)] = R\/4. - When two resistors R\u2081 and R\u2082 are connected in parallel, the resultant resistance R_eq is given by 1\/R_eq = 1\/R\u2081 + 1\/R\u2082 or R_eq = (R\u2081 * R\u2082) \/ (R\u2081 + R\u2082). - Plugging in the values, R_eq = (R * (R\/4)) \/ (R + R\/4) = (R\u00b2\/4) \/ (5R\/4). - R_eq = (R\u00b2\/4) * (4\/5R) = R\/5.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-copper-wire-of-radius-r-and-length-1-has-a-resistance-of-r-a-second\/#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":"A copper wire of radius r and length 1 has a resistance of R. A second"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/84649","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=84649"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/84649\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=84649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=84649"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=84649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}