Question

A wire of length L and area of cross section A has resistance 10 ohm. If the length is increased by 4 times. Find the new resistance keeping the volume constant.​

Answer 1

Given:

A wire of length L and area of cross section A has resistance 10 ohm. The length is increased by 4 times.

To find:

New resistance of the wire ?

Calculation:

Let initial length and area be l and a respectively.

$\therefore \: R = \rho \times \dfrac{l}{a}=10\:ohm \: \: \: \: \: \: ......(1)$

Now , new length is 4l and volume is constant.

$\therefore \:V1 = V2$

$\implies \: l \times a = 4l \times a_{2}$

$\implies \: a_{2} = \dfrac{a}{4}$

So, new resistance :

$\therefore \: R2 = \rho \times \dfrac{4l }{ a_{2} }$

$\implies \: R2 = \rho \times \dfrac{4l }{( \frac{a}{4} )}$

$\implies \: R2 =16 \times ( \rho \times \dfrac{l }{a} )$

$\implies \: R2 =16 \times (R)$

$\implies \: R2 =16 \times 10$

$\implies \: R2 =160 \: ohm$

So, new resistance is 160 ohm.