JEE Main 2025 Jan 22 Shift 2, Physics Q6: Capacitors And Capacitance

JEE Main2025Jan 22, Shift 2Physics

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
$[F] = [C^{2} M^{- 2} L^{2} T^{2}]$
B
$[F] = [C M^{- 2} L^{- 2} T^{- 2}]$
C
$[F] = [C M^{- 1} L^{- 2} T^{2}]$
D
$[F] = [C^{2} M^{- 1} L^{- 2} T^{2}]$

Solution

Capacitance is defined as $C = \frac{q}{V}$ , and potential $V = \frac{W}{q}$ where $W$ is work (energy).

So $C = \frac{q}{W / q} = \frac{q ^{2}}{W}$ .

In terms of base dimensions with charge as a fundamental: $[q] = C$ , $[W] = M L^{2} T^{- 2}$ .

$[C_{cap}] = \frac{C ^{2}}{M L ^{2} T ^{- 2}} = C^{2} M^{- 1} L^{- 2} T^{2}$ .

Concept behind this question

Capacitors And CapacitanceNotes, formulas and examples →

Practice more Physics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Jan 22 Shift 2, Physics Q6: Capacitors And Capacitance

Concept behind this question

More previous year questions on Capacitors And Capacitance

Practice more Physics