Question

The area of cross section of a wire becomes half when its length
is stretched to double. How the resistance of the wire is affected
in the new condition?
(a) Resistance of the wire remains unchanged
(b) Resistance of the wire decreases to half
(c) Resistance of the wire increases to double
(d) Resistance of the wire increases four times​

Answer 1

Answer:

option (d)

Explanation:

Given :

The area of cross section of a wire becomes half when its length  is stretched to double.

To find :

how the resistance of the wire is affected  in the new condition

Solution :

The resistance of a wire is given by,

 $\boxed{\longrightarrow \sf R=\dfrac{\rho l}{A}}$

where

ρ denotes the specific resistance (constant for a material)

l denotes the length of the wire

A denotes the area of cross section of the wire

• The area of cross section of the wire becomes half.

Let the new area be A'

A' = A/2

• The length of the wire is stretched to double.

Let the new length be l'

l' = 2l

Let the new resistance be R'

$\sf R'=\dfrac{\rho \times 2l}{\dfrac{A}{2}} \\\\ \sf R'=\dfrac{\rho \times 4l}{A} \\\\ \sf R'=4 \times \dfrac{\rho l}{A} \\\\ \sf R'=4R$

So, the resistance of the wire increases four times