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

Options

A. 50 rad/s and 25 rad/s
B. 46 rad/s and 54 rad/s
C. 42 rad/s and 58 rad/s
D. 25 rad/s and 75 rad/s

Answer

B

Explanation

`Q = omega/(Deltaomega) = (omega L)/R`
`rArr Deltaomega = R//L = 40/5 = 8` rad/sec
`omega_(0) = 1/sqrt(LC) = 1/sqrt(5 xx 80 xx 10^(-6)) = 50` rad/sec
`omega_("min") = omega_(0) - (Deltaomega)/2 = 46` rad/sec
`omega_("max") = omega_(0) -(Deltaomega)/2 = 54` rad/sec