Current Electricity

JEE Main level, single correct, medium

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Question 83 of 380

A uniform wire of length ll and radius rr has a resistance of 100Ω100 \text{Ω}. It is recast into a wire of radius r2\dfrac{r}{2}. The resistance of new wire will be-

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Answer: (A) 1600Ω1600\Omega

R=ρlAR=\rho \dfrac{l}{A}
Al=VAl=V
R=ρVA2R=\dfrac{\rho V}{{A}^{2}}
ρ→\rho \rightarrow constant
V→V\rightarrow constant
R∝1A2∝R\propto \dfrac{1}{{A}^{2}}\propto1(r2)2\dfrac{1}{{\left({r}^{2}\right)}^{2}}
R∝1r4R\propto \dfrac{1}{{r}^{4}}
R2=16R1=1600Ω{R}_{2}=16{R}_{1}=1600\Omega

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