8.2 Phasor representations

In section 7.x, we learned that the steady-state sinusoidal response of a linear circuit to a sinusoidal input was a sinusoidal output of the same frequency but with a different amplitude and phase.

For example, this circuit, with input Vmcos(2pif1t) produced output AVmcos(2pift+theta). The input and output are plotted on the same plot below. We see that the RC circuit changed both the amplitude and phase of the input but kept the phase the same,

Here we look at the phasor representations of voltages and currents and we define the  complex impedance as the ratio of phasor voltage to phasor current,. This is analogous to the resistance defined as ration of time-domain voltage to time-domain current,

Voltage and current for a resistor

time domain, phasor domain

Zr = Vr/Ir

Voltage and curent for a capacitor

Zc = Vc/Ic

indoctur

Zl=Vl/Il