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)

As, $C=\frac{\Delta q}{\Delta V}$
or ${\epsilon }_0=\frac{\left(\Delta q\right)L}{A\left(\Delta V\right)}...\left(i\right)$
$X={\epsilon }_{0}L=\frac{\Delta V}{\Delta t}$ (Given)
$\therefore X=\frac{\left(\Delta q\right)L}{A\left(\Delta V\right)}L\frac{\Delta V}{\Delta t}$ (Using $\left(i\right)$)
But $\left[A\right]={\left[L\right]}^2$
$\therefore X=\frac{\Delta q}{\Delta V}=$ current