Question

A copper wire is in the form of a cylinder and has resistance R. It is stretched till its thickness is reduced by half of its initial size. Find the new resistance in terms of R.

Answer 1

Given:

Shape of copper wire = Cylinder

Resistance = R

New size = 1/2 of initial size

To Find:

New resistance

Solution:

Initial volume = LA = Lπr²

Thickness is reduced by half = r = r/2

If we stretch wire till it is 1/2 of the initial size then it's length will increase four times.

New volume = LA = L'πr²

= Lπ(r/2)²

= Lπr²/4

= LA/4

As, volume should be constant, thus =  LA = LA/4 = LA

So L = 4L

Where, L is the length and A is the area.  

New resistance -

R = ρL/A

= ρ(4L)/(A/4)

= 16ρL/A

Answer: The new resistance is 16r