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Definition

When the source is a sinusoid of fixed frequency (we can have more than one source but the frequency must be the same), we replace the real voltage

$$V_m \cos (\omega t + \phi)$$

by the complex source  

$$V_m e^{j(\omega t + \phi)} = (V_m e^{j\phi}) e^{j\omega t} .$$

The complex number

$${\mathbf V} = V_m e^{j\phi} = V_m \angle \phi$$

is the phasor, where  

V_m is the magnitude.  

$\phi$ is the phase.  

This is illustrated in Figure 35, which shows the phasor V as a vector in the complex plane.

  

Figure 35: Phasor.

You can think of the phasor as a snap-shot at time zero of a vector rotating anticlockwise at angular speed $\omega$.

In AC analysis, we use phasor voltages and currents.

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