A uniform wire of resistance R is uniformly compressed along its length until its radius becomes n times the original radius. Now the resistance of the wire becomes

Question

A uniform wire of resistance R is uniformly compressed along its length until its radius becomes n times the original radius. Now the resistance of the wire becomes (A) (R/n4) (B) (R/n2) (C) (R/n) (D) nR

Tardigrade Admin · Accepted Answer

Volume before compression = Volume after compression i.e. π r2L = π(π r)2 L' i.e. L' = (L/n2)

Q. A uniform wire of resistance $R$ is uniformly compressed along its length until its radius becomes $n$ times the original radius. Now the resistance of the wire becomes

$\frac{R}{n ^{4}}$

$\frac{R}{n ^{2}}$

$\frac{R}{n}$

nR

Volume before compression = Volume after compression
$i . e .$ $π r^{2}$ L = $π (π r)^{2}$ L' $i . e .$ L' = $\frac{L}{n ^{2}}$

Q. A uniform wire of resistance R is uniformly compressed along its length until its radius becomes n times the original radius. Now the resistance of the wire becomes

n4R​

n2R​

nR​

nR

Volume before compression = Volume after compression i.e. πr2L = π(πr)2 L' i.e. L' = n2L​

Q. A uniform wire of resistance $R$ is uniformly compressed along its length until its radius becomes $n$ times the original radius. Now the resistance of the wire becomes

$\frac{R}{n ^{4}}$

$\frac{R}{n ^{2}}$

$\frac{R}{n}$

Volume before compression = Volume after compression
$i . e .$ $π r^{2}$ L = $π (π r)^{2}$ L' $i . e .$ L' = $\frac{L}{n ^{2}}$