Question

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

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

Answer 1

Answer: (D)

The dimensional formula for permittivity, $\left[\epsilon _{0}\right]=M^{- 1}L^{- 3}T^{4}A^{2}$ ,
dimensional formula for potential difference, $\left[\Delta V\right]=ML^{2}T^{- 3}A^{- 1}$ .
Hence, dimensional formula for $X=\epsilon _{0}L\frac{\Delta V}{\Delta t}=\left[M^{- 1} L^{- 3} T^{4} A^{2}\right]\left[L\right]\frac{\left[M L^{2} T^{- 3} A^{- 1}\right]}{\left[T\right]}=\left[A\right]$ .