A 20 Ω resistor, capacitor of reactance 25 Ω and inductor of reactance 45 Ω are connected in series to a 220 V (rms), 50 Hz AC source. Find rms current and phase angle between current and voltage.
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Question

A 20 Ω resistor, capacitor of reactance 25 Ω and inductor of reactance 45 Ω are connected in series to a 220 V (rms), 50 Hz AC source. Find rms current and phase angle between current and voltage.

G1 Physics · Accepted Answer

Step 1: The net reactance is X = Xₗ − X꜀ = 45 − 25 = 20 Ω, positive (inductive). Step 2: Series RLC impedance magnitude: Z = √[R² + (Xₗ − X꜀)²]. Step 3: Z = √(20² + 20²) = 20√2 Ω ≈ 28.284 Ω. Step 4: I(remainder)ₘₛ = Vᵣₘₛ/Z = 220/(20√2) ≈ 7.78 A. Step 5: tanφ = (Xₗ − X꜀)/R = 20/20 = 1, hence φ = 45°; current lags voltage. Final answer: 7.8 A and 45°, Option B.