Q. The specific resistance of a wire is $\rho$, its volume is $3\ m^{3}$ and its resistance is $3\Omega$, then its length will be
A) $\sqrt{\frac{1}{\rho}}$
B) $3/\sqrt{\rho}$
C) $\sqrt{3\ }/\rho$
D) $\rho/\sqrt{3}$
Explanation
(b) $R = \frac{\rho l}{A} = \frac{\rho l}{V/l} = \frac{\rho l^{2}}{V}$
or $l = \left( \frac{RV}{\rho} \right)^{1/2} = \left( \frac{3 \times 3}{\rho} \right)^{1/2} = \frac{3}{\sqrt{\rho}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.