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# Series (Phase) Resonance

Series resonance is defined1 as "the steady-state condition which exists in a circuit comprising inductance and capacitance connected in series, when the current in the circuit is in phase with the voltage across the circuit." From this definition the input impedance of the circuit at resonance is equivalent to pure resistance. This is often called series resonance, or merely resonance. The term voltage resonance is sometimes used, a term applicable only if the effective resistance is negligible.

Resonance occurs in a series circuit when the inductive reactance XL = 2πfL equals the capacitive reactance Xc = l/(2πfC). Thus,

where f is the (phase) resonant frequency in cycles per second when L is the inductance in henrys and C is the capacitance in farads. For the practical case a series circuit is composed of an inductor having effective resistance R and a capacitor having negligible loss. The resistance does not affect the frequency of resonance. The way in which the input impedance varies with frequency is shown in Fig. 9. Note that the input impedance is low at resonance.

At resonance the current in a series-resonant circuit is limited only by the effective resistance of the coil. If the coil has a low effective resistance (a high Q), the current may rise to a high value, and large reactive voltages (Ex = IXC = IXL approximately) will exist across the capacitor and inductor. This principle is used to increase signal voltages.

Last Update: 2011-05-30