Inductor in series and parallel

We shall first consider an ideal voltage source applied to the series combination of N inductors.

Applying KVL to the original circuit,

V_s = V₁ + V₂ + … + V_n

But for the equivalent circuit we have,

And thus the equivalent inductance is

L_eq = (L₁ + L₂ + … + L_N)

i_s = i₁ + i₂ + … + i_n

We know that