Question

A quantity X is given by $\varepsilon _{0} L =\frac{\Delta V}{\Delta t}$, where $e_0$ 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)

current

Answer 2

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