A series LCR circuit containing 5.0 H inductor, 80 μ F capacitor and 40 Ω 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:

Question

A series LCR circuit containing 5.0 H inductor, 80 μ F capacitor and 40 Ω 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: (A) 25 rad / s and 75 rad / s (B) 50 rad / s and 25 rad / s (C) 46 rad / s and 54 rad / s (D) 42 rad / s and 58 rad / s

Tardigrade Admin · Accepted Answer

beginarrayl Q =(ω/Δ ω)=(ω L / R ) ⇒ Δ ω= R / L =(50/4)=8 rad / sec ω0=(1/√ LC )=(1/√5 × 80 × 10-6)=50 rad / sec ω min =ω0-(Δ ω/2)=46 rad / sec ω max =ω0-(Δ ω/2)=54 rad / sec endarray

Q. A series LCR circuit containing $5.0 H$ inductor, $80 μ F$ capacitor and $40 Ω$ 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:

$25 r a d / s$ and $75 r a d / s$

$50 r a d / s$ and $25 r a d / s$

$46 r a d / s$ and $54 r a d / s$

$42 r a d / s$ and $58 r a d / s$

$Q = \frac{ω}{Δ ω} = \frac{ω L}{R} \Rightarrow Δ ω = R / L = \frac{50}{4} = 8 r a d / sec ω_{0} = \frac{1}{L C} = \frac{1}{5 \times 80 \times 1 0 ^{- 6}} = 50 r a d / sec ω_{m i n} = ω_{0} - \frac{Δ ω}{2} = 46 r a d / sec ω_{m a x} = ω_{0} - \frac{Δ ω}{2} = 54 r a d / sec$

Q. A series LCR circuit containing 5.0H inductor, 80μF capacitor and 40Ω 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:

25rad/s and 75rad/s

50rad/s and 25rad/s

46rad/s and 54rad/s

42rad/s and 58rad/s