{"id":87661,"date":"2025-06-01T06:50:46","date_gmt":"2025-06-01T06:50:46","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87661"},"modified":"2025-06-01T06:50:46","modified_gmt":"2025-06-01T06:50:46","slug":"let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/","title":{"rendered":"Let us consider a copper wire having radius r and length l. Let its re"},"content":{"rendered":"

Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l\/2 then the resistance of this wire will be<\/p>\n

[amp_mcq option1=”R” option2=”2R” option3=”R\/4″ option4=”R\/8″ correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is (D) R\/8.
\n<\/section>\n
\nThe resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = \u03c1(l\/A), where \u03c1 is the resistivity of the material. The cross-sectional area of a wire with radius r is A = \u03c0r\u00b2.
\n<\/section>\n
\nLet the initial resistance be R. R = \u03c1 * (l \/ (\u03c0r\u00b2)).
\nFor the second wire, the radius is r’ = 2r and the length is l’ = l\/2.
\nThe new cross-sectional area A’ = \u03c0(r’)\u00b2 = \u03c0(2r)\u00b2 = \u03c0(4r\u00b2) = 4\u03c0r\u00b2.
\nThe new resistance R’ = \u03c1 * (l’ \/ A’) = \u03c1 * ((l\/2) \/ (4\u03c0r\u00b2)).
\nR’ = \u03c1 * (l \/ (8\u03c0r\u00b2)) = (1\/8) * [\u03c1 * (l \/ (\u03c0r\u00b2))].
\nSince R = \u03c1 * (l \/ (\u03c0r\u00b2)), we have R’ = R\/8.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l\/2 then the resistance of this wire will be [amp_mcq option1=”R” option2=”2R” option3=”R\/4″ option4=”R\/8″ correct=”option4″] This question was previously asked in UPSC NDA-1 – 2019 … <\/p>\n

Detailed SolutionLet us consider a copper wire having radius r and length l. Let its re<\/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":[1093],"tags":[1119,1201,1128],"class_list":["post-87661","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1119","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nLet us consider a copper wire having radius r and length l. Let its re<\/title>\n<meta name=\"description\" content=\"The correct answer is (D) R\/8. The resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = \u03c1(l\/A), where \u03c1 is the resistivity of the material. The cross-sectional area of a wire with radius r is A = \u03c0r\u00b2.\" \/>\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\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Let us consider a copper wire having radius r and length l. Let its re\" \/>\n<meta property=\"og:description\" content=\"The correct answer is (D) R\/8. The resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = \u03c1(l\/A), where \u03c1 is the resistivity of the material. The cross-sectional area of a wire with radius r is A = \u03c0r\u00b2.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:50:46+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":"Let us consider a copper wire having radius r and length l. Let its re","description":"The correct answer is (D) R\/8. The resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = \u03c1(l\/A), where \u03c1 is the resistivity of the material. The cross-sectional area of a wire with radius r is A = \u03c0r\u00b2.","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\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/","og_locale":"en_US","og_type":"article","og_title":"Let us consider a copper wire having radius r and length l. Let its re","og_description":"The correct answer is (D) R\/8. The resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = \u03c1(l\/A), where \u03c1 is the resistivity of the material. The cross-sectional area of a wire with radius r is A = \u03c0r\u00b2.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:50:46+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\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/","url":"https:\/\/exam.pscnotes.com\/mcq\/let-us-consider-a-copper-wire-having-radius-r-and-length-l-let-its-re\/","name":"Let us consider a copper wire having radius r and length l. 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