Question

A quantity $X$ is given by ${ϵ}_{0}L\frac{\Delta V}{\Delta t}$, where ${ϵ}_0$ is the permittivity of fee space, $L$ is length, $\Delta V$ is a potential difference and $\Delta t$ is a time interval. The dimensional formula for $X$ is the same as that of

• A. resistance
• B. charge
• C. voltage
• D. current

Answer 1

The correct option is D current

Dimensional formula for ${ϵ}_0=\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]$
Dimensional formula for $L=\left[L\right]$
Dimensional formula for $\Delta V=\left[M{L}^2{T}^{-3}{I}^{-1}\right]$
Dimensional formula for $\Delta t=\left[T^1\right]$
Therefore, dimensional formula for $X$ is: $\frac{\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]\left[L\right]\left[M{L}^2{T}^{-3}{I}^{-1}\right]}{\left[T^1\right]}=\left[I\right]$

Therefore, its the same as that of current.