Question

The specific resistance of a wire is $\rho$. If its volume is $3 m ^{3}$ and its resistance is 3 ohms, then its length will be

• A. $\sqrt{\frac{1}{\rho}}$
• B. $\frac{3}{\sqrt{\rho}}$
• C. $\frac{1}{\rho} \sqrt{3}$
• D. $\rho \sqrt{\frac{1}{3}}$

Answer 1

Answer: (B)

Volume $=A l=3 \Rightarrow A=\frac{3}{l}$
Now $R=\rho \frac{l}{A} \Rightarrow 3=\frac{\rho \times l}{3 / l}=\frac{\rho l^{2}}{3} $
$\Rightarrow l^{2}=\frac{9}{\rho}=\frac{3}{\sqrt{\rho}}$