Q. Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M,$ of length $L,$ of time $T$ and current $I,$ would be
A) $\left\lbrack {ML}^{2}T^{- 3}I^{- 1} \right\rbrack$
B) $\left\lbrack {ML}^{2}T^{- 2} \right\rbrack$
C) $\left\lbrack {ML}^{2}T^{- 1}I^{- 1} \right\rbrack$
D) $\left\lbrack {ML}^{2}T^{- 3}I^{- 2} \right\rbrack$
Explanation
Resistance, $R = \frac{Potential\ difference}{Current} = \frac{V}{i} = \frac{W}{q^{i}}$ $(\because Potential\ difference\ is\ equal\ to\ work\ doen\ per\ unit\ charge)$ So, dimensions of $R$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\lbrack Dimensions\ of\ work\rbrack}{\lbrack Dimensions\ of\ charge\rbrack\lbrack Dimensions\ of\ current\rbrack}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\left\lbrack ML^{2}T^{- 2} \right\rbrack}{\lbrack IT\rbrack\lbrack I\rbrack} = \left\lbrack ML^{2}T^{- 3}I^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.