Question

Resistance of a metal wire of length 10 cm is 2 ohm.
If the wire is stretched uniformly to 50 cm, the
resistance is
(a) 25 ohm
(b) 10 ohm
(c) 5 ohm

(d) 50 ohm

Answer it correctly.

Answer 1

Given:

• Initial resistance is 2 ohm.
• Length is stretched uniformly from 10 cm to 50 cm.

To find:

New resistance ?

Calculation:

• Since the wire is stretched, the volume of the wire will remain constant .

$V1 = V2$

$\implies \: A_{1} l_{1} = A_{2} l_{2}$

$\implies \: A_{1} \times 10 = A_{2} \times 50$

$\implies \: A_{2} = \dfrac{A_{1} }{5}$

Now, new resistance will be :

$R_{2} = \rho \times \dfrac{ l_{2} }{A_{2}}$

$\implies R_{2} = \rho \times \dfrac{ 50}{ \dfrac{A_{1}}{5}}$

$\implies R_{2} = 25 \times ( \rho \times \dfrac{ 10}{ A_{1}} )$

$\implies R_{2} = 25 \times R_{1}$

$\implies R_{2} = 25 \times 2$

$\implies R_{2} = 50 \: ohm$

So, new resistance is 50 ohm (option d)