NEETPhysicsAlternating Current
A series LCR circuit with inductance L = 0.1 H and capacitance C = 10 F is connected across various voltage sources. Match the voltage sources in List-I with the corresponding steady-state behavior of the circuit in List-II. List-I List-II (A) V = V₀ (1000t) (I) Current leads the voltage (B) V = V₀ (500t) (II) Current lags the voltage (C) V = V₀ (2000t) (III) Current is in phase with the voltage (D) 10 V DC source (I
Options
- A(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
- B(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
- C(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
- D(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
Correct answer
A. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
Step-by-step solution
The resonant angular frequency of the LCR circuit is: ₀ = 1 LC = 1 0.1 10 10⁻⁶ = 1000 rad s ⁻¹ (A) For V = V₀ (1000t) , = 1000 rad s ⁻¹ . Since = ₀ , the circuit is at resonance and the current is in phase with the voltage. (A) matches with (III). (B) For V = V₀ (500t) , = 500 rad s ⁻¹ . Since (C) For V = V₀ (2000t) , = 2000 rad s ⁻¹ . Since > ₀ , inductive reactance X_L is greater than capacitive reactance X_C . The circuit is inductive, so the current lags the voltage. (C) matches with (II). (D) For a 10 V DC sou