Q. The dimensions of resistance are same as those of ………. Where $h$ is the Planck’s constant and $e$ is the charge.
A) $\frac{h^{2}}{e^{2}}$
B) $\frac{h^{2}}{e}$
C) $\frac{h}{e^{2}}$
D) $\frac{h}{e}$
Explanation
Resistance, $R = \frac{V}{i} = \frac{W}{qi}$ $\ \ \ \ \ \ \ \ \ = \frac{\left\lbrack {ML}^{2}T^{- 2} \right\rbrack}{\left\lbrack A^{2}T \right\rbrack}$ $\ \ \ \ \ R = \left\lbrack {ML}^{2}T^{- 3}A^{- 2} \right\rbrack$ $\left\lbrack \frac{h}{e^{2}} \right\rbrack = \frac{\left\lbrack {ML}^{2}T^{- 1} \right\rbrack}{\lbrack AT\rbrack^{2}}$ $\ \ \ \ \ \ \ \ \ = \left\lbrack {ML}^{2}T^{- 3}A^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.