A wire is connected to a battery and has a certain current flowing through it. If the radius of a wire were doubled, what would happen to the current?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n If the radius of a wire is doubled while connected to the same battery, the current flowing through the wire will increase. Specifically, the current will increase by a factor of four.<\/p>\n\n\n\n Here is the explanation:<\/p>\n\n\n\n The current II in a wire depends on the voltage VV supplied by the battery and the resistance RR of the wire, according to Ohm\u2019s Law: I=VRI = \\frac{V}{R}<\/p>\n\n\n\n The resistance RR of a wire is determined by the resistivity \u03c1\\rho of the material, the length LL of the wire, and the cross-sectional area AA of the wire: R=\u03c1LAR = \\frac{\\rho L}{A}<\/p>\n\n\n\n For a wire with a circular cross-section, the area AA is: A=\u03c0r2A = \\pi r^2<\/p>\n\n\n\n where rr is the radius of the wire.<\/p>\n\n\n\n If the radius of the wire is doubled, the new radius becomes 2r2r. The new cross-sectional area A\u2032A’ is: A\u2032=\u03c0(2r)2=\u03c0\u00d74r2=4\u00d7\u03c0r2=4AA’ = \\pi (2r)^2 = \\pi \\times 4r^2 = 4 \\times \\pi r^2 = 4A<\/p>\n\n\n\n Because resistance is inversely proportional to the area, the new resistance R\u2032R’ is: R\u2032=\u03c1LA\u2032=\u03c1L4A=R4R’ = \\frac{\\rho L}{A’} = \\frac{\\rho L}{4A} = \\frac{R}{4}<\/p>\n\n\n\n With the resistance reduced to one quarter of its original value and the battery voltage unchanged, the current increases by a factor of four: I\u2032=VR\u2032=VR\/4=4\u00d7VR=4II’ = \\frac{V}{R’} = \\frac{V}{R\/4} = 4 \\times \\frac{V}{R} = 4I<\/p>\n\n\n\n Therefore, doubling the radius of the wire causes the current to increase four times, assuming the battery voltage and wire length remain constant. This is because a thicker wire has less resistance, allowing more current to flow through it under the same voltage.<\/p>\n","protected":false},"excerpt":{"rendered":" A wire is connected to a battery and has a certain current flowing through it. If the radius of a wire were doubled, what would happen to the current? The correct answer and explanation is: If the radius of a wire is doubled while connected to the same battery, the current flowing through the wire […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-35428","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=35428"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35428\/revisions"}],"predecessor-version":[{"id":35430,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35428\/revisions\/35430"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}