A wire of given material having length l and area of cross-section Ahas a resistance of 4 โฆ. What would be the resistance of another wireof the same material having length l/2 and area of cross-section 2A?
Last updated at Aug. 6, 2019 by Teachoo
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Example 12.6 A wire of given material having length l and area of cross-section A has a resistance of 4 โฆ. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A? We know that Resistance of a wire = ๐ ๐/๐ด where ๐ = resistivity of the material l = length of the wire A = Area of cross-section of wire It is given that R = 4 ฮฉ โด ๐ ๐/๐ด = 4 Now, For the second wire Length of the wire = ๐2 = ๐/2 Area of cross โ section = A2 = 2A Resistivity = ๐ Finding resistance, R2 = ๐ ๐_2/๐ด_2 R2 = ๐ (๐/2) ร 1/2๐ด (because the material is same) R2 = ๐๐/๐ด (1/2ร1/2) R2 = ๐๐/๐ด (1/4) R2 = 4 ร 1/4 R2 = 1 ฮฉ Resistance of second wire is 1 ฮฉ
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