Question

The specific resistance of a wire is $\rho$, its volume is $3{\text{m}}^3$ and its resistance is $3\Omega$, 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

The correct option is B $\frac{3}{\sqrt{\rho }}$

Let $A$ be area of cross section,
$l$ be length of wire.

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