Question

A quantity X is given by $ \varepsilon _{0} L =\frac{\Delta V}{\Delta t} $, where $ε_0$ 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 $\varepsilon_{0} = \frac{\left(\Delta q\right)L}{A\left(\Delta V\right)} \quad...\left(i\right)$
$X = \varepsilon _{0} L =\frac{\Delta V}{\Delta t}$ (Given)
$\therefore \quad X = \frac{\left(\Delta q\right)L}{A\left(\Delta V\right)} L \frac{\Delta V}{\Delta t} \quad$ (Using $\left(i\right)$)
But $\left[A\right] = \left[L\right]^{2}$
$\therefore \quad X = \frac{\Delta q}{\Delta V} =$ current