An $$LCR$$  series circuit is connected to a source of alternating current. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of

Solution :
A circuit in which inductance $$L,$$ capacitance $$C$$ and resistance $$R$$ are connected in series, and the circuit admits maximum current corresponding to a given frequency of $$AC$$ is called series resonance circuit. The impedance $$\left( Z \right)$$ of an $$RLC$$  circuit is given by
$$Z = \sqrt {{R^2} + {{\left( {\omega L - \frac{1}{{\omega C}}} \right)}^2}} $$
At resonance $${X_L} = {X_C}$$
i.e. $$\omega L = \frac{1}{{\omega C}},Z = R$$
So, circuit behaves as if it contains $$R$$ only. So, phase difference $$= 0.$$
Frequency of resonating $$LCR$$  circuit is given by
$$\eqalign{ & {\omega ^2} = \frac{1}{{LC}} \cr & \Rightarrow f = \frac{1}{{2\pi \sqrt {LC} }} \cr} $$