AC Circuit Containing Inductance Only

Let an alternating voltage E = E₀ ejωt be applied across an inductance L. Let I be the instantaneous current and dI/dt be the rate of change of current with time through the inductance.


The voltage induced across the inductance = L dI/dt.
Or            dI = E₀/L e jωt dt

Integration,         I = E₀/jωL e jωt = E/ jω                            … (1)

. :            I = E₀/ωL e j(ωt – π/2)
The actual current in the circuits is
            I = I₀ sin (ωt – π/2)                            … (2)

In a pure inductor, the current lags behind the emf by π/2.