Question

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

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

Answer 1

The correct option is B 3$\sqrt{\frac{1}{\rho }}$

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