Question 461: AC fundamentals

Question

A series LCR circuit containing 5.0 H inductor, 80$$\mu$$F capacitor and 40$$\Omega$$ resistor is connected to 230V 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 :

Accepted Answer

$$Q = {\omega  \over {\Delta \omega }} = {{\omega L} \over R} \Rightarrow \Delta \omega  = R/L = {{50} \over 4} = 8$$ rad/sec
$${\omega _0} = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {5 	imes 80 	imes {{10}^{ - 6}}} }} = 50$$ rad/sec
$${\omega _{\min }} = {\omega _0} - {{\Delta \omega } \over 2} = 46$$ rad/sec
$${\omega _{\max }} = {\omega _0} - {{\Delta \omega } \over 2} = 54$$ rad/sec

Answer

42 rad/s and 58 rad/s

Answer

25 rad/s and 75 rad/s

Answer

50 rad/s and 25 rad/s

Answer

46 rad/s and 54 rad/s

AC fundamentals

A series LCR circuit containing 5.0 H inductor, 80$\muF capacitor and 40\Omega$ resistor is connected to 230V 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 :

Choose the correct answer: