Parallel Resonant Circuits

Author: J.B. Hoag

Fig. 6 B shows a parallel circuit and its impedance curves.

Fig. 6 B. A parallel circuit and its impedance curve

The curves are of the same shape as the current curves of a series circuit. Note that the impedance across the terminals of a parallel circuit is a maximum at resonance,¹ whereas it is a minimum for the series circuit. The current in the LCR circuit itself is often very large at resonance and can cause considerable heating.

The impedance of a parallel circuit at resonance is given by

if all the resistance is in the coil (which is very nearly true in practice). The meaning of Q is given in Section 6.4. The resonant frequency f_r is given by the same equation as for a series circuit provided R is small in comparison with X. This is often true in radio frequency circuits.

1	There are really three different ways of defining resonance in the case of a parallel circuit, but, if the resistance is low, the resonant frequency in all three cases is practically identical.