Question

A quantity X is given by ${\epsilon }_{o}L\frac{\Delta V}{\Delta L}$ where ${\epsilon }_o$ is the permittivity of free space. L is a 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

Given,

$X={ϵ}_{0}L\frac{\Delta V}{\Delta L}$

Dimensional formula for ${ϵ}_0=\left[M^{-1}{L}^{-3}{T}^3{I}^2\right]$

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 $X=\frac{\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]\left[L\right]\left[M{L}^2{T}^{-3}{I}^{-1}\right]}{\left[T^1\right]}=\left[I\right]$

So, the dimensional formula of $X$ is same as that of current.