Question

A wire of resistance $R=4\Omega$ is stretched, so that its radius decreases to be a factor n=5. calculate its new resistance.

• A. $4\Omega$
• B. $2.5k\Omega$
• C. $2k\Omega$
• D. $5\Omega$

Answer 1

The correct option is B $2.5k\Omega$

Initial resistance of the wire $R=\frac{\rho V}{A^2}$ where $A=\pi r^2$

$⟹$ $R=\frac{\rho V}{{\pi }^2{r}^4}$

Given : $R=4\Omega$ $r^{\prime }=r/5$

New resistance of the wire $R^{\prime }=\frac{\rho V}{{\pi }^2(r/5{)}^4}=5^{4}R=5^4\times 4=2.5k\Omega$