Pure inductor (coil of zero ohmic resistance)

When AC flows in a coil, the current changes continuously, so a back emf −L ΔI/Δt is induced by self-induction; it opposes the source emf and has the same frequency. Applying Kirchhoff's second law for a coil with negligible resistance, the source voltage balances the induced emf: V = L ΔI/Δt.

• The voltage is proportional to the rate of change of current (the slope of the I–t curve): it is maximum when the current passes through zero (steepest slope) and zero when the current is at maximum (zero slope); it is negative when the current is decreasing.
• Plotting the slope gives a curve shifted by a quarter of a cycle.
• Therefore:

In an inductor the voltage leads the current by 90° (equivalently, the current lags the voltage by 90°).