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

Answer 1

`16\Omega`

Step-by-step 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`

`(L_0)/(L)=(A)/(A_0)`...(1)

`R=\rho(l)/(A)`

Using the formula

`1=(\rho L_0)/(A_0)`

`R=(\rho L)/(A)`

Using equation (1)

`(1)/(R)=(L_0A)/(LA_0)=(A)/(A_0)* (A)/(A_0)=((A)/(A_0))^2`

Area , A=
`\pi r^2`

Substitute the values

`(1)/(R)=((\pi (0.25r_0)^2)/(\pi(r_0)^2))^2=0.0625`

`R=(1)/(0.0625)=16\Omega`