A wire is stretched so as to change its diameter by `0.25%` . The percentage change in resistance is

Options

A. `4.0%`
B. `2.0%`
C. `1.0%`
D. `0.5%`

Answer

C

Explanation

On stretching, volume (V) remains constant.
So, V = Al or l = V/A
Now, `R=(rho l)/(A)=(rho V)/(A^(2))=(rho V)/(pi^(2)D^(4)//16)=(16rho V)/(pi^(2)D^(4))`
Taking logarithm of both the side and differentiating it, we get
`(Delta R)/(R )=-4 (Delta D)/(D)`
or `(Delta R)/(R )=-4xx(-0.25)=1.0%`