Question Detail
Question
Series RLC: R=10Ω, L=0.5H, C=10μF, source 100V, 50Hz. Impedance and phase angle?
Correct Answer
Option D is the correct answer.
Detailed Explanation
X_L = 2πfL = 2π×50×0.5 = 157.1 Ω. X_C = 1/(2πfC) = 1/(2π×50×10×10⁻⁶) = 1/0.0031416 = 318.3 Ω. X_L - X_C = -161.2 Ω. Z = √(R² + (X_L-X_C)²) = √(100 + 25986) = √26086 = 161.5 Ω. tanφ = (X_L-X_C)/R = -161.2/10 = -16.12 → φ = -86.5°.
Hint
Z = √(R² + (X_L-X_C)²), φ = arctan((X_L-X_C)/R).