A circuit containing reactance is said to be in resonance if the voltage across the circuit is in phase with the current through it. At resonance, the circuit thus behaves as a pure resistor and the net reactance is zero.

Consider the series R-L-C circuit as shown in Fig. 1. 

Fig. 1 Series Circuit

The impedance of the circuit is

$\bar Z=R+jX_L-jX_C\\ \ \ \ = R+j\omega L-j\dfrac{1}{\omega C}\\ \ \ \ =R+j\Bigg(\omega L-\dfrac{1}{\omega C}\Bigg)$

At resonance, Z must be resistive. Therefore the condition for resonance is,

$\omega L-\dfrac{1}{\omega C}=0\\ w=\omega _0=\dfrac{1}{\sqrt {LC}}\\ f=f_o=\dfrac{1}{2\pi \sqrt {LC}}$

Where, f0 is called the resonant frequency of the circuit.

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