Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

Step 1: Formula for Capacitance

Capacitance $C$ is defined as:

$$C = \frac{Q}{V}$$

where:

• $Q$ is charge (unit: coulomb, $C$),
• $V$ is voltage (unit: volt, $V$).

From the definition of voltage:

$$V = \frac{W}{Q}$$

where:

• $W$ is work (or energy, with unit joule),
• $Q$ is charge.

Thus, voltage:

$$V = \frac{M L^2 T^{-2}}{Q}$$

Step 2: Dimensional Formula for Capacitance

Since $C = \frac{Q}{V}$, we substitute the dimensional formulas:

$$[C] = \frac{C}{M L^2 T^{-2} / C}$$

 $$[C] = \frac{C^2 T^2}{M L^2}$$

$\left[\mathrm{F}\right]=\left[{\mathrm{C}}^2{\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^2\right]$