Leading and lagging current

In this type of circuit, the terms lead, lag, and in phase are used to describe current with reference to voltage.

It can also play an important role in the operation of three phase electric power systems.

Angle notation can easily describe leading and lagging current:

[1] In this equation, the value of theta is the important factor for leading and lagging current.

As mentioned in the introduction above, leading or lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or behind of where it would be initially.

[2] Using complex numbers is a way to simplify analyzing certain components in RLC circuits.

, the angle of the current sine wave with respect to an arbitrarily chosen reference, is less than

In circuits with primarily inductive loads, current lags the voltage.

This happens because in an inductive load, it is the induced electromotive force that causes the current to flow.

The induced electromotive force is caused by a change in the magnetic flux linking the coils of an inductor.

, the angle of the current sine wave with respect to an arbitrarily chosen reference is greater than

In circuits with primarily capacitive loads, current leads the voltage.

This is true because current must first flow to the two plates of the capacitor, where charge is stored.

Only after charge accumulates at the plates of a capacitor is a voltage difference established.

In the real-complex coordinate system, one period of a sine wave corresponds to a full circle in the complex plane.

Since the voltage and current have the same frequency, at any moment in time those quantities can be easily represented by stationary points on the circle, while the arrows from the center of circle to those points are called phasors.

[2] An early source of data is an article from the 1911 American Academy of Arts and Sciences by Arthur E. Kennelly.