Q. If $L,\ C\ and\ R$ denote inductance, capacitance and resistance respectively, then which of the following combination has the dimension of time?
A) $\frac{C}{L}$
B) $\frac{1}{RC}$
C) $\frac{L}{R}$
D) $\frac{RL}{C}$
Explanation
Dimensions of $L\ and\ R$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack R\rbrack = \left\lbrack {ML}^{2}T^{- 3}A^{- 2} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack L\rbrack = \lbrack ML^{2}T^{- 2}\ A^{- 2}\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\lbrack \frac{L}{R} \right\rbrack = \frac{\left\lbrack ML^{2}T^{- 2}A^{- 2} \right\rbrack}{\left\lbrack ML^{2}T^{- 3}A^{- 2} \right\rbrack}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \lbrack T\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.