In the chapters on inductance and capacitance we have learned that both conditions are reactive and can provide opposition to currentflow, but for opposite reasons. Therefore, it is important to find the point where inductance and capacitance cancel one another to achieve efficient operation of AC circuits.

EO 1.15 DEFINE resonance.

EO 1.16 Given the values of capacitance (C) and inductance (L), CALCULATE the resonant frequency.

EO 1.17 Given a series R-C-L circuit at resonance, DESCRIBE the net reactance of the circuit.

EO 1.18 Given a parallel R-C-L circuit at resonance, DESCRIBE the circuit output relative to current (I).

Resonant Frequency

Resonance occurs in an AC circuit when inductive reactance and capacitive reactance are equal to one another: X_L = X_c. When this occurs, the total reactance, X = X_L - X_cbecomes zero and the impendence is totally resistive. Because inductive reactance and capacitive reactance are both dependent on frequency, it is possible to bring a circuit to resonance by adjusting the frequency of the applied voltage. Resonant frequency (f_Res) is the frequency at which resonance occurs, or where X_L = X_c. Equation (8-14) is the mathematical representation for resonant frequency.

where

Series Resonance

In a series R-C-L circuit, as in Figure 9, at resonance the net reactance of the circuit is zero, and the impedance is equal to the circuit resistance; therefore, the current output of a series resonant circuit is at a maximum value for that circuit and is determined by the value of the resistance. (Z=R)