Dimensions of Impedance

Dimensional Formula of Impedance

The dimensional formula of Impedance is given by,

M¹ L² I^-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 = [I¹ T¹] . . . (4)

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

V = [M¹ L¹ T^-2] × [I¹ T¹]^-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 L² I^-2 T^-3]

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

⇒ Check Other Dimensional Formulas:

• Dimensions of Universal Gravitational Constant
• Dimensions of Density
• Dimensions of Specific Heat Capacity
• Dimensions of Impedance
• Dimensions of Gravitational Potential Energy

Impedance – JEE Concept Alternating Current