Resonance frequency — UPSC CSE 1995 Physics PYQ

An alternating voltage of varying frequency is applied across a two-branch parallel circuit of R_1 and L in series and R_2 and C in series as shown in Fig. below.

Find its resonant frequency. If R_1 and R_2 are not zero, state the conditions when the resonant frequency is given by f_0 = \frac{1}{2\pi \sqrt{LC}}