An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are conne

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Question

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts. Potential difference across L, C and R is 40 V, 10 V and 40 V respectively. The amplitude of current flowing through the LCR series circuit is 10√2 A. The impedance of the circuit is

Accepted Answer

Correct Answer: A — 5 ΩStep-by-step Solution:Step 1: Find the RMS source voltage using phasor addition.Vrms = √(V_R² + (V_L - V_C)²) = √(40² + (40 - 10)²) = √(1600 + 900) = √2500 = 50 V.Step 2: Find RMS current from given amplitude.Irms = Ipeak / √2 = (10√2) / √2 = 10 A.Step 3: Calculate impedance.Z = Vrms / Irms = 50 / 10 = 5 Ω.Why other options are incorrect: Option B (4√2 ≈ 5.66 Ω) results from using incorrect phasor addition. Option C (2.5 Ω) uses the amplitude directly without converting to RMS. Option D (4 Ω) does not follow from correct phasor computation.Key Concept: In a series LCR circuit, impedance Z = Vrms/Irms, and Vrms = √(V_R² + (V_L - V_C)²). Ipeak = √2 × Irms.

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