A RLC circuit has a frequency (called the resonant frequency} where its response is strongest (largest current) when excited by an external source whose frequency matches its resonant frequency. The current in the circuit is the source voltage V divided by the circuit impedance Z _V 17 For a given source voltage V, the largest current occurs at the frequency where the impedance is smallest. The impedance is by denio'on l' ' r r Z: vz +(AL AC}2 Since Z is the square root of the sum of two squares (two positive numbers], it is smallest when the two squares are smallest. The resistance R is unchanged with frequency, but the reactance term does change with frequency. At the frequency where the reactance is O, that is the smallest 2 {hence largest current]. So the resonant frequency of the circuit is determined by the equation XL 'c: = 0 From the denition of inducve reactance XL and capacitive reactanceXC show that the resonance frequency is _ l ff\" _ mm