A series LCR circuit has R = 10 ohm, L = 0.1 H, and C = 100 μF. If the frequency of the AC source is 50 Hz, what is the impedance?
Q1. A series LCR circuit has R = 10 ohm, L = 0.1 H, and C = 100 μF. If the frequency of the AC source is 50 Hz, what is the impedance?
Answer: 10 ohm
Explanation: Xl = 2πfL = 2 * 3.14 * 50 * 0.1 = 31.4 ohm. Xc = 1 / (2πfC) = 1 / (2 * 3.14 * 50 * 100 * 10^(-6)) = 31.85 ohm. Z = √(R² + (Xl - Xc)²) = √(10² + (31.4 - 31.85)²) = √(100 + (-0.45)²) = √(100 + 0.2025) = √100.2025 = 10.01 ≈ 10 but closest is 17.9 - some value, actually Z = √(100 + 0.2) = 10.