Inductance has the dimension of

Expressions for Self-inductance:

• The property of a coil that opposes any change in the amount of current flowing through it is called its self-inductance or inductance.

Factors affecting inductance

• The greater the self-induced voltage, the greater the self-inductance of the coil, and hence larger is the opposition to the changing current.
• According to Faraday’s laws of electromagnetic induction, induced voltage in a coil depends upon the number of turns (N) and the rate of change of flux (dφ/dt) linking the coil.
   

Hence, the inductance of a coil depends upon these factors:

• Shape and number of turns.
• Relative permeability of the material surrounding the coil.
• The speed with which the magnetic field changes.
   

Consider an iron-cored solenoid of dimensions as shown in Fig.

The inductance of the solenoid (L) is given by,

\(L=N\frac{dϕ}{dI}\)

Now, flux (ϕ) = \(\frac{NI}{S}=\frac{NI}{l/a\mu_0 \mu_r}\)

Where, NI is MMF and S is reluctance,

Differentiating ϕ wrt I,

\(\frac{d\phi}{dI}=\frac{Na\mu_0\mu_r}{l}\)

Now, \(L=N\frac{dϕ}{dI}=N\frac{Na\mu_0\mu_r}{l}=\frac{N^2}{S}\)

Now, inductive reactance (XL) = ωL = \(\dfrac{\omega N^2}{S}\)

Conclusion:

From the above concept,

Inductance has the dimension of Flux/current.