JEE Physics 2025 Question with Solution

Given: We need the dimensional formula of capacitance in $\text{F}$.

Find: The correct dimensional expression in terms of $M$, $L$, $T$ and $C$.

Capacitance is defined as

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

where $Q$ is charge and $V$ is potential difference.

Potential difference is

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

where energy has dimensions

$$[U] = [ML^2T^{-2}]$$

So,

$$[V] = \frac{[ML^2T^{-2}]}{[C]}$$

Therefore, the dimensional formula of capacitance is

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

which gives

$$[C] = [CM^{-1}L^{-2}T^2]$$

Therefore, the correct option is A.

Given: Capacitance $C$ is related to charge and potential difference.

Find: Its dimensional formula.

1. Start from the definition

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

2. Write potential difference in terms of energy:

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

3. The dimensional formula of work or energy is

$$[W] = [ML^2T^{-2}]$$

4. Hence,

$$[V] = [ML^2T^{-2}C^{-1}]$$

5. Now substitute into the capacitance formula:

$$[C] = \frac{[Q]}{[V]} = \frac{[C]}{[ML^2T^{-2}C^{-1}]}$$

6. On simplification,

$$[C] = [CM^{-1}L^{-2}T^2]$$

So the dimensional formula of capacitance is $[CM^{-1}L^{-2}T^2]$, and the correct option is A.