## Quick Reference

A reactive circuit (see reactance) so arranged that it is capable of resonance. In a **series resonant circuit** a resistor, inductor, and capacitor are arranged in series. Resonance occurs when the impedance (*Z*) is a minimum and the current amplitude therefore a maximum. In a **parallel resonant circuit** the inductance and capacitance are in parallel and resonance (with minimal current amplitude) occurs at maximum impedance. The frequency at which resonance occurs is called the **resonant frequency**. In a series resonant circuit *Z* = *R* + i[ω*L* − 1/ω*C*], where ω = 2π*f* and *f* is the frequency, *R* is the resistance, *L* is the inductance, and *C* is the capacitance. At resonance, *Z* is a minimum and ω*L* = 1/ω*C*, i.e. the circuit behaves as if it is purely resistive. In the parallel circuit, resonance occurs when *R*^{2} + ω^{2}*L*^{2} = *L*/*C*, which in most cases also approximates to ω*L* = 1/ω*C*. Resonant circuits are widely used in radio to select one signal frequency in preference to others.

*Z* = *R* + i[ω*L* − 1/ω*C*],

*Subjects:*
Physics.