## The resistance of a wire of lengt L0 and radius r0 is 1 ohm If the wire is stretched so thay its radius becomes 0.25r0. what is the new resi

Question

The resistance of a wire of lengt L0 and radius r0 is 1 ohm If the wire is stretched so thay its radius becomes 0.25r0. what is the new resistance of the wire

in progress 0
1 year 2021-09-05T16:08:25+00:00 1 Answers 27 views 0

$$16\Omega$$

Explanation:

Initial length of wire=$$L_0$$

Initial radius of wire=$$r_0$$

Resistance of wire=1 ohm

After stretching

Radius of wire=r=$$0.25r_0$$

New resistance  of wire=R

When the wire drawn under tensile stress  then volume remains constant.

$$V=A_0L_0=AL$$

$$\frac{L_0}{L}=\frac{A}{A_0}$$…(1)

$$R=\rho\frac{l}{A}$$

Using the formula

$$1=\frac{\rho L_0}{A_0}$$

$$R=\frac{\rho L}{A}$$

Using equation (1)

$$\frac{1}{R}=\frac{L_0A}{LA_0}=\frac{A}{A_0}\times \frac{A}{A_0}=(\frac{A}{A_0})^2$$

Area , A=$$\pi r^2$$

Substitute the values

$$\frac{1}{R}=(\frac{\pi (0.25r_0)^2}{\pi(r_0)^2})^2=0.0625$$

$$R=\frac{1}{0.0625}=16\Omega$$