# Dimensions of Impedance

## Dimensional Formula of Impedance

The dimensional formula of Impedance is given by,

M1 LI-2 T-3

Where,

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

### Derivation

Impedance (Z) = Voltage × [Electric Current]-1 . . . . (1)

Since, Voltage = Electric Field × Distance

V = Force × [Electric Charge]-1 × Distance . . (2)

⇒ The dimensions of force = [M1 L1 T-2] . . . (3)

And, the dimensional formula of electric charge = [IT1] . . . (4)

On substituting equation (3) and (4) in equation (2) we get,

V = [M1 L1 T-2] × [IT1]-1 × [M0 L1 T0]

∴ The dimensional formula of voltage = [M1 L2 I-1 T-3] . . . . (5)

And, the dimensions of Electric Current = [M0 L0 I-1 T0] . . . . . (6)

On substituting equation (5) and (6) in equation (1) we get,

Impedance = Voltage × [Electric Current]-1

Or, Z = [M1 L2 I-1 T-3] × [M0 L0 I1 T0]-1 = [M1 LI-2 T-3]

Therefore, impedance is dimensionally represented as M1 L2 I-2 T-3.