Let an alternating emf E = E0e^jωt be applied to a circuit having an inductance L and a non-inductive resistance R in series.
The potential drop across the inductance is
        V_L = jωL I
The potential drop across resistance is
        V_R = RI
Here, I is the current at any instant t.
. :         E = jωL I + RI
Current in the circuit,
        I = E/R + jωL                                    … (1)
But        I = E/Z                                        … (2)
Impedance of R-L circuit,
        Z = R + jωL                                    … (3)
. :        I = E₀ ejωt/√(R² + ω²L²) e^jθ                     (where tan θ = ωL/R)
        = E₀ /√R2 + ω2L2) ej(ωt – 0)                            … (4)
        = I₀ e^j(ωt-θ)                                     … (5)
Here,        I₀ = E₀ /√R² + ω²L²)                                 … (6)

It represents the peak value of the current through the circuit.

The impedance Z of the circuit is given by the term
        √(R² + ω²L²).

The current lags in phase behind the emf by an angle θ = tan^-1 ωL/R.
The variation of instantaneous values of emf and current with time are represented graphically.


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