Q. The physical quantity having the dimensions $\left\lbrack M^{- 1}L^{- 3}A^{2} \right\rbrack$ is

A) Resistance
B) Resistivity
C) Electrical conductivity
D) Electromotive force
Explanation

Resistivity, $\rho = \frac{m}{ne^{2}\tau}$ $\therefore\lbrack\rho\rbrack = \frac{\lbrack M\rbrack}{\left\lbrack L^{- 3} \right\rbrack\lbrack AT\rbrack\left\lbrack T^{2} \right\rbrack}$ $= \left\lbrack {ML}^{3}A^{- 2}T^{- 3} \right\rbrack$ So, electrical conductivity $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sigma = \frac{1}{\rho}$ $\Rightarrow \ \ \ \ \ \ \ \ \ \ \lbrack\sigma\rbrack = \frac{1}{\lbrack\rho\rbrack} = \left\lbrack M^{- 1}L^{- 3}A^{2}T^{3} \right\rbrack\$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.