Q. A quantity $X$ is given by $\varepsilon_{0}L\frac{\mathrm{\Delta}V}{\mathrm{\Delta}t},\$where $\varepsilon_{0}$ is the permittivity of free space, $L$ is a length, $\mathrm{\Delta}V$ is a potential difference and $\mathrm{\Delta}t$ is a time interval. The dimensional formula for $X$ is the same as that of
A) Electrical resistance
B) Electric charge
C) Electric voltage
D) Electric current
Explanation
Dimensions of $\varepsilon_{0} = \left\lbrack M^{- 1}L^{- 3}T^{4}A^{2} \right\rbrack$ Dimensions of $L = \lbrack L\rbrack$ Dimensions of $\mathrm{\Delta}V = \left\lbrack ML^{2}T^{- 3}A^{- 1} \right\rbrack$ Dimensions of $\mathrm{\Delta}t = \lbrack T\rbrack$ As $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ X = \varepsilon_{0}L\frac{\mathrm{\Delta}V}{\mathrm{\Delta}t}$ Dimensions of $X = \frac{\left\lbrack M^{- 1}L^{- 3}T^{4}A^{2} \right\rbrack\lbrack L\rbrack\left\lbrack ML^{2}T^{- 3}A^{- 1} \right\rbrack}{\lbrack T\rbrack}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \lbrack A\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.