NEET2021PhysicsAlternating CurrentActual
A series L - C - R 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:
Options
- A25   rad   s - 1   and  75   rad   s - 1
- B50   rad   s - 1  and  25   rad   s - 1
- C46   rad   s - 1  and  54   rad   s - 1
- D42   rad   s - 1  and  58   rad   s - 1
Correct answer
C. 46   rad   s - 1  and  54   rad   s - 1
Step-by-step solution
L = 5 H , C = 80 μ F , R = 40 ω ;   V = 230   V Resonance angular frequency = ω 0 = 1 L C = 1 5 × 80 × 10 - 6 = 50   rad   s - 1 Half power angular frequency = ω 0 ± R 2 L = 50 ± 40 2 × 5 = 50 ± 4 = 54   or   46 We get, ω 1 = 46   rad   s - 1 And ω 2 = 54   rad   s - 1