Phase Relationship in Pure Inductive AC Circuits

In an AC circuit containing an ideal (pure) inductor, the relationship between the voltage across the inductor and the current flowing through it is crucial.

Inductor Behavior in AC Circuits

• A pure inductor resists changes in current. In an AC circuit, this resistance manifests as a phase shift between the voltage and the current.
• Specifically, the current flowing through a pure inductor lags behind the applied voltage across it.

Calculating the Phase Lag

The phase difference ($\phi$) between voltage and current in a pure inductive circuit is:

• In radians: $\phi = \frac{\pi}{2}$
• In degrees: $\phi = 90^\circ$

A full cycle in an AC waveform corresponds to $2\pi$ radians or $360^\circ$. To express the phase lag as a fraction of a cycle, we calculate:

Fraction = $\frac{\text{Phase Lag}}{\text{Full Cycle}} = \frac{\pi/2}{2\pi} = \frac{1}{4}$

Alternatively, using degrees:

Fraction = $\frac{90^\circ}{360^\circ} = \frac{1}{4}$

Conclusion

Therefore, the current flowing through a pure inductor in an AC circuit lags the applied voltage by a quarter of a cycle.