Question

A wire has a resistance of $24\Omega$. If the length of the wire is tripled, then the resistance of the wire will become -

• A. $24\Omega$
• B. $\frac{24}{3}\Omega$
• C. $216\Omega$
• D. $250\Omega$

Answer 1

The correct option is C $216\Omega$

Volume of the wire will not change on changing its length.

$\Rightarrow Al=A^{\prime }{l}^{\prime }$

$\Rightarrow Al=A^{\prime }\left(3l\right)$

$\Rightarrow A^{\prime }=\frac{A}{3}$

So, new resistance,

$R^{\prime }=\rho \frac{l^{\prime }}{A^{\prime }}=\rho \frac{3l}{A/3}=9\rho \frac{l}{A}=9R$

$\Rightarrow R^{\prime }=9\times 24=216\Omega$

Hence, option $\left(C\right)$ is the correct answer.