In order to quadruple the resistance of a wire of uniform cross-section, a fraction of its length was uniformly stretched till the final length of the entire wire was 1-5 times the initial length. The fraction is
Resistance of a wire is given by
R = ρ L/A . When stretched, L ′ = 1.5L and = A/(1.5)², so
new resistance:
R ′ = ρ 1.5L/A/(1.5)² = 2.25R
To make R′ = 4R, solving gives fraction
1/6. Answer: (c) 1/6.
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