NEET 2025 Physics Impedance and Phase Angle MCQ Question
To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively -
7.8 Å and 30°
7.8 Å and 45°
15.6 Å and 30°
15.6 Å and 45°
Correct Answer
Detailed Explanation
The correct option is (2) 7.8 A and 45°.
Explanation: This is a series RLC circuit with:
Resistance R = 20 Ω Capacitive reactance X_C = 25 Ω Inductive reactance X_L = 45 Ω Supply voltage V_rms = 220 V (AC, frequency 50 Hz not needed since reactances are already given)
Step 1: Calculate net reactance X = X_L − X_C = 45 − 25 = 20 Ω (The circuit is inductive overall because X_L > X_C)
Step 2: Calculate impedance Z Z = √(R² + X²) = √(20² + 20²) = √(400 + 400) = √800 = √(16 × 50) = 4√50 = 20√2 ≈ 28.28 Ω
Step 3: Calculate rms current I I = V / Z = 220 / (20√2) = 220 / (20 × 1.4142) ≈ 220 / 28.284 ≈ 7.78 A (Rounded to one decimal place → 7.8 A)
Step 4: Calculate phase angle φ tan φ = X / R = 20 / 20 = 1 φ = tan⁻¹(1) = 45° Since X > 0 (inductive), current lags voltage by 45° (phase angle is 45° lagging).
Final answer: Current ≈ 7.8 A and phase angle = 45° → Option (2) 7.8 A and 45° is correct. (Option 4 has 15.6 A which would occur if someone mistakenly took Z = √(20² + (45−25)²) wrong or used only R, but calculation confirms 7.8 A.)
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