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In an experiment, 200 V A.C. is applied at the ends of an LCR circuit. The circuit consists of an inductive reactance (Xₗ) = 50 Ω, capacitive reactance (Xₐ) = 50 Ω and ohmic resistance (R) = 10 Ω. The impedance of the circuit is

1. 10 Ω
2. 20 Ω
3. 30 Ω
4. 40 Ω

Correct answer: 10 Ω

Solution

In an LCR circuit, the impedance (Z) is given by Z = √(R² + (Xₗ - Xₐ)²). Here, R = 10 Ω, Xₗ = 50 Ω, and Xₐ = 50 Ω. Since Xₗ = Xₐ, the net reactance (Xₗ - Xₐ) = 0. Thus, Z = √(10² + 0²) = 10 Ω.

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