{"id":88012,"date":"2025-06-01T06:59:37","date_gmt":"2025-06-01T06:59:37","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88012"},"modified":"2025-06-01T06:59:37","modified_gmt":"2025-06-01T06:59:37","slug":"in-an-electric-circuit-a-wire-of-resistance-10-%cf%89-is-used-if-this-wir","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/in-an-electric-circuit-a-wire-of-resistance-10-%cf%89-is-used-if-this-wir\/","title":{"rendered":"In an electric circuit, a wire of resistance 10 \u03a9 is used. If this wir"},"content":{"rendered":"

In an electric circuit, a wire of resistance 10 \u03a9 is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :<\/p>\n

[amp_mcq option1=”half of its original value.” option2=”double of its original value.” option3=”one-fourth of its original value.” option4=”four times of its original value.” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe resistance of a wire depends on its material (resistivity), length, and cross-sectional area. When a wire is stretched, its length increases, and its cross-sectional area decreases, while its volume remains constant. This change in dimensions affects the resistance. The current in the circuit is inversely proportional to the resistance (assuming constant voltage).
\n<\/section>\n
\n– Resistance R = $\\rho \\frac{L}{A}$, where $\\rho$ is resistivity, L is length, and A is cross-sectional area.
\n– Volume of the wire V = A \u00d7 L. When stretched, the volume remains constant: $A’L’ = AL$.
\n– Ohm’s Law: Current I = Voltage V \/ Resistance R.
\n<\/section>\n
\nLet the original length be L and the original cross-sectional area be A. The original resistance is $R = \\rho \\frac{L}{A}$.
\nThe wire is stretched to a new length $L’ = 2L$.
\nSince the volume remains constant, $A’L’ = AL$.
\n$A'(2L) = AL \\Rightarrow A’ = \\frac{A}{2}$.
\nThe new resistance is $R’ = \\rho \\frac{L’}{A’} = \\rho \\frac{2L}{A\/2} = \\rho \\frac{2L \\times 2}{A} = 4 \\rho \\frac{L}{A}$.
\nSo, $R’ = 4R$. The resistance becomes four times the original resistance.
\nAssuming the voltage V across the circuit element (or the voltage source) is constant:
\nOriginal current $I = \\frac{V}{R}$.
\nNew current $I’ = \\frac{V}{R’} = \\frac{V}{4R} = \\frac{1}{4} \\left(\\frac{V}{R}\\right) = \\frac{1}{4}I$.
\nThe current in the circuit would become one-fourth of its original value.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

In an electric circuit, a wire of resistance 10 \u03a9 is used. If this wire is stretched to a length double of its original value, the current in the circuit would become : [amp_mcq option1=”half of its original value.” option2=”double of its original value.” option3=”one-fourth of its original value.” option4=”four times of its original value.” … <\/p>\n

Detailed SolutionIn an electric circuit, a wire of resistance 10 \u03a9 is used. If this wir<\/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":[1105,1201,1128],"class_list":["post-88012","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1105","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nIn an electric circuit, a wire of resistance 10 \u03a9 is used. If this wir<\/title>\n<meta name=\"description\" content=\"The resistance of a wire depends on its material (resistivity), length, and cross-sectional area. When a wire is stretched, its length increases, and its cross-sectional area decreases, while its volume remains constant. This change in dimensions affects the resistance. The current in the circuit is inversely proportional to the resistance (assuming constant voltage). - Resistance R = $rho frac{L}{A}$, where $rho$ is resistivity, L is length, and A is cross-sectional area. - Volume of the wire V = A \u00d7 L. When stretched, the volume remains constant: $A'L' = AL$. - Ohm's Law: Current I = Voltage V \/ Resistance R.\" \/>\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\/in-an-electric-circuit-a-wire-of-resistance-10-\u03c9-is-used-if-this-wir\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In an electric circuit, a wire of resistance 10 \u03a9 is used. If this wir\" \/>\n<meta property=\"og:description\" content=\"The resistance of a wire depends on its material (resistivity), length, and cross-sectional area. When a wire is stretched, its length increases, and its cross-sectional area decreases, while its volume remains constant. This change in dimensions affects the resistance. The current in the circuit is inversely proportional to the resistance (assuming constant voltage). - Resistance R = $rho frac{L}{A}$, where $rho$ is resistivity, L is length, and A is cross-sectional area. - Volume of the wire V = A \u00d7 L. When stretched, the volume remains constant: $A'L' = AL$. - Ohm's Law: Current I = Voltage V \/ Resistance R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/in-an-electric-circuit-a-wire-of-resistance-10-\u03c9-is-used-if-this-wir\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:59:37+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":"In an electric circuit, a wire of resistance 10 \u03a9 is used. 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