Representing AC Voltages and Currents as Vectors
In AC circuit analysis, every sinusoidal voltage or current can be depicted as a vector. The vector’s length equals the waveform’s amplitude (or RMS value), while its direction encodes the phase angle relative to a reference waveform.
Below is a diagram illustrating how the amplitude of a sinusoid is translated into the length of its corresponding vector.
Increasing the waveform’s amplitude stretches the vector; the angle, measured in degrees, represents the phase shift between the waveform of interest and a chosen reference. In most cases, the reference is the main AC supply voltage, which is arbitrarily set to 0°.
Because phase is inherently a relative measure, it only gains meaning when compared against another waveform. For instance, if the supply voltage leads a load current by 45°, the current vector will be rotated 45° clockwise from the voltage vector.
Just as a grounded node provides a common voltage reference in a circuit, an arbitrarily chosen waveform serves as the phase reference. This convention allows us to state, for example, that a current of 24.3 mA lags the reference by 64°, written as “24.3 mA at –64°”.
Review
- When describing an AC quantity, the vector’s length represents its amplitude, and its angle represents the phase relative to a reference waveform.
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