1Which is the dimensional formula of capacitance?
Capacitance works out to [M⁻¹ L⁻² T⁴ A²].
ElectrostaticsClass 12, Electrostatic Potential and Capacitance
Dimensional formula of Capacitance
[M-1 L-2 T4 A2]
Charge stored per volt, C = Q/V.
How to get the dimensional formula of capacitance
- Start from the definition: capacitance = electric charge / electric potential.
- electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- electric potential = energy / electric charge, so electric potential is [M L2 T-2] / [T A] = [M L2 T-3 A-1].
- Put in the dimension of each part: [T A] / [M L2 T-3 A-1].
- Add the powers of each base quantity: [M-1 L-2 T4 A2].
Three questions on capacitance
2What is the SI unit of capacitance?
The SI unit of capacitance is the farad (F).
3Do capacitance and volume charge density have the same dimensions?
Capacitance is [M⁻¹ L⁻² T⁴ A²] but volume charge density is [L⁻³ T A].
An equation that uses capacitance
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
C = ε0 A / dC[M-1 L-2 T4 A2]=epsilon0 A / d[M-1 L-2 T4 A2]Dimensionally consistentEvery term is [M-1 L-2 T4 A2]
ε0 = permittivity of free space
Capacitance: quick answers
What is the dimensional formula of capacitance?
The dimensional formula of capacitance is [M⁻¹ L⁻² T⁴ A²]. It comes from capacitance = electric charge / electric potential.
What is the SI unit of capacitance?
The SI unit of capacitance is the farad (F).
Is capacitance dimensionless?
No. Capacitance has the dimensions [M⁻¹ L⁻² T⁴ A²].