Question

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ___$\%$.

Answer 1

Answer: 300

$V^{\prime }=V$
${\ell }^{\prime }A=\ell A$
$2\ell A^{\prime }=\ell A$
$A^{\prime }=\frac{A}{2}$
$R=\rho \frac{\ell }{A}\dots$ (i)
${\ell }^{\prime }=2\ell$
$A^{\prime }=\frac{A}{2}$
$R^{\prime }=\frac{\rho {\ell }^{\prime }}{A^{\prime }}=\frac{\rho 2\ell }{\frac{A}{2}}$
$R^{\prime }=\frac{4\rho \ell }{A}$
$R^{\prime }=4R$ from equation (i)
$\%$ increase in resistance
$=\frac{R^{\prime }-R}{R}\times 100=\frac{4R-R}{R}\times 100$
$=300\%$