Question

A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

(1) 25 rad/s and 75 rad/s

(2) 50 rad/s and 25 rad/s

(3) 46 rad/s and 54 rad/s

(4) 42 rad/s and 58 rad/s

Answer 1

Correct option is (3) 46 rad/s and 54 rad/s

The resonance frequency of LCR series circuit is given as,

\(\omega _0 = \frac 1{\sqrt{LC}}\)

\( = \frac 1{\sqrt {5\times 80 \times 10^{-6}}} \)

= 50 rad/s

Now, half power frequencies are given as,

\(\omega =\omega _0\pm \frac R{2L}\)

So,

\(\omega_L = 50 - \frac{40 }{2\times 5}\)

= 46 rad/s

\(\omega_H = 50 + \frac{40 }{2\times 5}\)

= 54 rad/s

Answer 2

Option : (3) 46 rad/s and 54 rad/s