 # Dimensions of Capacitance

## Dimensional Formula of Capacitance

The dimensional formula of Capacitance is given by,

M-1 L-2 T4 I2

Where,

• M = Mass
• I = Current
• L = Length
• T = Time

### Derivation

Capacitance (C) = Charge × Voltage-1 . . . . (1)

Since, Charge = Current × Time

∴ The dimensional formula of charge = [I1 T1] . . . . (2)

And, Voltage = Electric Field × Distance . . (3)

Electric Field = [Force × Charge-1]

The dimensional formula of force and charge is [M1 L1 T-2] and [I1 T1] respectively.

∴ The dimensional formula of Electric Field =  [M1 L1 T-2] × [I1 T1]-1

= [M1 L1 T-3 I-1] . . . (4)

On substituting equation (4) in equation (3) we get,

The dimensional formula of Voltage = [M1 L1 T-3 I-1] × [L1] = [M1 L2 T-3 I-1] . . . . (5)

On substituting equation (5) and (2) in equation (1) we get,

Capacitance = Charge × Voltage-1

Or, C = [I1 T1] × [M1 L2 T-3 I-1]-1 = [M-1 L-2 TI2]

Therefore, the Capacitance is dimensionally represented as [M-1 L-2 TI2].

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