NEETPhysicsAlternating Current
A series LCR circuit with inductance L = 50 mH , capacitance C = 20 F , and resistance R = 40 is connected to a variable frequency AC source of 200 V (rms). What is the angular frequency of the source at which the power dissipated in the circuit is maximum, and what is the value of this maximum power?
Options
- A1000 rad s ⁻¹ and 2000 W
- B100 rad s ⁻¹ and 1000 W
- C1000 rad s ⁻¹ and 500 W
- D1000 rad s ⁻¹ and 1000 W
Correct answer
D. 1000 rad s ⁻¹ and 1000 W
Step-by-step solution
Maximum power dissipation in a series LCR circuit occurs at resonance, where the impedance is purely resistive and minimum ( Z = R ). The resonant angular frequency is given by: _r = 1 LC Substituting the given values: _r = 1 50 10⁻³ 20 10⁻⁶ _r = 1 1000 10⁻⁹ = 1 10⁻⁶ = 1000 rad s ⁻¹ At resonance, the maximum power dissipated is: P_ max = V_ rms ^2 R Substituting the given values: P_ max = (200)^2 40 = 40000 40 = 1000 W Answer: 1000 rad s ⁻¹ and 1000 W