In general, the equivalent impedance seen at any pair of terminals can be written in rectangular form as

In a passive circuit the equivalent resistance REQ must always be nonnegative, that is, REQ ≥ 0. However, the equivalent reactance XEQ can be either positive (inductive)
or negative (capacitive). When inductance and capacitance are both present, their reactances may exactly cancel at certain frequencies. When XEQ = 0, the impedance is purely resistive and the circuit is said to be in resonance. The frequency at which this occurs is called a resonant frequency, denoted by ω0.
For example, suppose we want to find the resonant frequency of the circuit in Figure8–25.Wefirst findtheequivalent impedanceof theparallel resistorandcapacitor

This expression can be put into rectangular form by multiplying and dividing by the conjugate of the denominator

Transcribed Image Text:

ZEQ = REQ+jXEQ