Question

A wire has a resistance of 10 ohm. Its resistance if it is stretched by one-tenth of its original length is:

• A. $12.1$ $\Omega$
• B. $7.9$ $\Omega$
• C. $11$ $\Omega$
• D. $9$ $\Omega$

Answer 1

Answer: (A)

$12.1$ $\Omega$

The resistance, $R$, of a wire of length $l$ is given by,
$R=\frac{\rho l}{A}$.

Now if the wire is stretched keeping the volume intact then:
$R=\frac{\rho l^2}{V}$.

Now $R\propto l^2$. According to the question, we get,

$\frac{R_2}{R_1}=\frac{(l_2{)}^2}{({l_1)}^2}$
But $R_1=10\Omega ,\frac{l_2}{l_1}=\frac{11}{10}$.
$\Rightarrow \frac{R_2}{10}=\frac{121}{100}$

$\Rightarrow R_2=12.1\Omega$