Physics

Problem

For a series

RLC

circuit the phase angle between the supply voltage and current is

+\phi

at angular frequency

\omega_1

and

-\phi

at angular frequency

\omega_2

. a. (i) Prove that

\omega_1\,\omega_2 = \omega_0^{\,2}

, where

\omega_0

is the resonant angular frequency of the circuit. b. (ii) A circuit has

R = 20\,\Omega

L = 50\,\text{mH}

and

C = 0.50\,\mu\text{F}

. Calculate

\omega_1

and

\omega_2

when

\phi = 60^{\circ}

(take

\tan60^{\circ}=\sqrt{3}