Question

What happens to the resistance of a wire if the radius r is changed into 2r

Answer 1

Answer:

Let us find out the resistance when the radius is r

$\mathsf{Resistance = \rho \frac{L}{A}}$

$\mathsf{R = \rho \frac{L}{2\pi r}\:\rightarrow (1)}$

If the radius is doubled i.e 2r

$\mathsf{New\:Resistance = \rho \frac{L}{A}}$

$\mathsf{R' = \rho \frac{L}{2\pi . 2r}}$

$\mathsf{R' = \rho \frac{L}{2\pi r}×\frac{1}{2}}$

$\mathsf{R' = R × \frac{1}{2}}$ {using (1) }

$\mathsf{R' = \frac{R}{2}}$

Hence, the resistance reduces to half