Question

The below figure shows a series resonant circuit energised by a sinusoidal 10V rms source. In all calculations below, use approximations if they are appropriate.

(i) What is the resonant angular frequency of the circuit with the component values as given above?

(ii) What is the Q factor of the circuit?

(iii) What are the half-power angular frequencies of the circuit?

(iv) What current passes through the 30 $\Omega$ resistance at resonance?

A resistor of 6 $\Omega$ is now connected between terminals A and B. (v) What is the resonant angular frequency now?

(vi) What power is dissipated in the 6 $\Omega$ resistor at the resonant angular frequency?

Answer 1

i)   resonant angular frequency of the circuit = 1/sqrt(LC)

                                                                       =   1/sqrt(0.1 * 12.355 * 10^-6)

                                                                      =   899.66 rad/sec

ii)   Q factor of the circuit =    (1/R) * sqrt(L/C)

                                        =   (1/30) * sqrt(0.1/12.355 * 10^-6)

                                         =   3

iii)   half-power angular frequencies of the circuit =>

Here, R/2L = 30/(2 * 0.1)   =   150 rad/sec

=>   half-power angular frequencies of the circuit = 749.66 rad/sec   and    1049.66 rad/sec

iv)    current passes through the 30 $\Omega$ resistance at resonance = 10/30 =   0.333 A

v)      resonant angular frequency now = 1/sqrt(0.1 * 12.355 * 10^-6)

                                                                =   899.66 rad/sec

vi)     power is dissipated in the 6 $\Omega$ resistor   =   (10/6)² * 6

                                                                        = 16.66 W