Question

A wire of resistance $10.0\Omega$ is stretched and increases its length by $20\%$. Its resistance then would be: $($ neglect any change in volume or resistivity $)$

• A. $10.0\Omega$
• B. $12.0\Omega$
• C. $14.4\Omega$
• D. $10.2\Omega$

Answer 1

The correct option is B $12.0\Omega$

Let $R$ be the resistance of wire, $L$ be its length. $R^{{}^{\prime }}$ be the resistance of wire after stretching and $L^{{}^{\prime }}$ is length of the wire after stretching.
We know,
$R=\frac{\rho L}{A}$ ........................................(1)
and
$R^{{}^{\prime }}=\frac{\rho L^{{}^{\prime }}}{A}$
where variables have their usual meanings.
Here $L^{{}^{\prime }}=L+\frac{L}{5}$
Hence,
$R^{{}^{\prime }}=\frac{\rho (L+\frac{L}{5})}{A}$ ...............................(2)

Performing $eq\left(2\right)/eq\left(1\right)$

$R^{{}^{\prime }}=\frac{L+\frac{L}{5}}{L}R$
$R^{{}^{\prime }}=\frac{6}{5}R$

$R^{{}^{\prime }}=12\Omega$