JEE Main 2025 · 22 January · evening · Single correct · +4 / −1
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,
- (a) [F]=[CM⁻¹ L⁻² T²]
- (b) [F]=[C² M⁻² L² T²]
- (c) [F]=[C² M⁻¹ L⁻² T²]
- (d) [F]=[CM⁻² L⁻² T⁻²]
Answer and solution
Answer (c) [F]=[C² M⁻¹ L⁻² T²]
Solution
Physics sir · 3 steps
Capacitance is charge over voltage, and voltage itself hides a charge, so charge ends up squared.
- Start from definition. Capacitance is charge stored per volt, F = Q/V. So first find the dimensions of voltage. In this question the letter C is the dimension of charge, not capacitance.
- Dimensions of voltage. Voltage is work done per unit charge, V = W/Q. Work has dimensions [M L² T⁻²], so [V] = [M L² T⁻² C⁻¹].
[F] = [Q]/[V] = [C]/[M L² T⁻² C⁻¹] = [C² M⁻¹ L⁻² T²]
- So. Dividing by C⁻¹ multiplies by C, so charge appears squared and every other power flips sign. The answer is (c).
The idea to keep. For any electrical quantity, rewrite it through charge and energy: V = W/Q, F = Q/V. Then the charge powers fall out automatically and you do not have to memorise anything.
Answer from the NTA final answer key. Solution by PrepWiser.