{"id":88172,"date":"2025-06-01T07:03:55","date_gmt":"2025-06-01T07:03:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88172"},"modified":"2025-06-01T07:03:55","modified_gmt":"2025-06-01T07:03:55","slug":"the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/","title":{"rendered":"The resistance of a wire of length \/ and area of cross-section a is x"},"content":{"rendered":"

The resistance of a wire of length \/ and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become:<\/p>\n

[amp_mcq option1=”2x ohm” option2=”0.5 x ohm” option3=”4x ohm” option4=”6x ohm” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-2 – 2015<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l’ = 2l), its volume (V = a * l) remains constant. So, a’ * l’ = a * l => a’ * (2l) = a * l => a’ = a\/2. The new resistance is R’ = \u03c1 * (l’\/a’) = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x.<\/section>\n
When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.<\/section>\n
The resistance is directly proportional to length and inversely proportional to cross-sectional area. Stretching the wire affects both parameters simultaneously.<\/section>\n","protected":false},"excerpt":{"rendered":"

The resistance of a wire of length \/ and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become: [amp_mcq option1=”2x ohm” option2=”0.5 x ohm” option3=”4x ohm” option4=”6x ohm” correct=”option3″] This question was previously asked in UPSC NDA-2 – 2015 Download PDFAttempt Online The resistance … <\/p>\n

Detailed SolutionThe resistance of a wire of length \/ and area of cross-section a is x<\/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":[1094],"tags":[1443,1201,1128],"class_list":["post-88172","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1443","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nThe resistance of a wire of length \/ and area of cross-section a is x<\/title>\n<meta name=\"description\" content=\"The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l' = 2l), its volume (V = a * l) remains constant. So, a' * l' = a * l => a' * (2l) = a * l => a' = a\/2. The new resistance is R' = \u03c1 * (l'\/a') = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x. When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.\" \/>\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\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The resistance of a wire of length \/ and area of cross-section a is x\" \/>\n<meta property=\"og:description\" content=\"The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l' = 2l), its volume (V = a * l) remains constant. So, a' * l' = a * l => a' * (2l) = a * l => a' = a\/2. The new resistance is R' = \u03c1 * (l'\/a') = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x. When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:03:55+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":"The resistance of a wire of length \/ and area of cross-section a is x","description":"The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l' = 2l), its volume (V = a * l) remains constant. So, a' * l' = a * l => a' * (2l) = a * l => a' = a\/2. The new resistance is R' = \u03c1 * (l'\/a') = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x. When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.","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\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/","og_locale":"en_US","og_type":"article","og_title":"The resistance of a wire of length \/ and area of cross-section a is x","og_description":"The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l' = 2l), its volume (V = a * l) remains constant. So, a' * l' = a * l => a' * (2l) = a * l => a' = a\/2. The new resistance is R' = \u03c1 * (l'\/a') = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x. When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:03:55+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\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/","name":"The resistance of a wire of length \/ and area of cross-section a is x","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:03:55+00:00","dateModified":"2025-06-01T07:03:55+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The resistance (R) of a wire is given by R = \u03c1 * (l\/a), where \u03c1 is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l' = 2l), its volume (V = a * l) remains constant. So, a' * l' = a * l => a' * (2l) = a * l => a' = a\/2. The new resistance is R' = \u03c1 * (l'\/a') = \u03c1 * (2l \/ (a\/2)) = \u03c1 * (4l\/a) = 4 * (\u03c1 * l\/a) = 4x. When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-resistance-of-a-wire-of-length-and-area-of-cross-section-a-is-x\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"The resistance of a wire of length \/ and area of cross-section a is x"}]},{"@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\/88172","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=88172"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88172\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}