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 T⁴ I²]

Therefore, the Capacitance is dimensionally represented as [M^-1 L^-2 T⁴ I²].

⇒ Check Other Dimensional Formulas:

• Dimensions of Newton
• Dimensions of Momentum
• Dimensions of Pressure Gradient
• Dimensions of Rotational Kinetic Energy
• Dimensions of Gravitational Potential Energy