First slide

Ohm's law

Question

The resistance of a wire is ‘R’ ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be

Moderate

A

$\frac{R}{n}$
B

$n^{2} R$
C

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

nR

Solution

The resistance of a wire of length l and area A and resistivity $ρ$ is given as
$R = \frac{ρ l}{A}$
$Given, l^{'} = n l$
As the volume of the wire remains constant
$∴ A^{'} l^{'} = A l$
$A^{'} = \frac{A l}{l^{'}} = \frac{A l}{n l} or A^{'} = \frac{A}{n}$
$∴ R^{'} = \frac{ρ l^{'}}{A^{'}} = \frac{ρ n l}{\frac{A}{n}} = \frac{n^{2} ρ l}{A} = n^{2} R$

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