Question Detail
Question
A given RLC circuit has R=100Ω, L=1H and C=10µF all connected in series with a source of 200sin ωt with ω = 400 rad/s. Calculate the phase angle and determine the circuit type.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Given:Resistance (R) = 100 ΩInductance (L) = 1 HCapacitance (C) = 10 µF = 10 x 10⁻⁶ FAngular frequency (ω) = 400 rad/s1. Calculate Inductive Reactance (X_L):X_L = ωL = 400 rad/s * 1 H = 400 Ω2. Calculate Capacitive Reactance (X_C):X_C = 1 / (ωC) = 1 / (400 rad/s * 10 x 10⁻⁶ F) = 1 / (4 x 10⁻³) Ω = 250 Ω3. Determine the circuit type:Since X_L (400 Ω) > X_C (250 Ω), the circuit is inductive.4. Calculate the phase angle (φ):φ = arctan((X_L - X_C) / R)φ = arctan((400 Ω - 250 Ω) / 100 Ω)φ = arctan(150 Ω / 100 Ω)φ = arctan(1.5)φ ≈ 56.3°Thus, the phase angle is approximately 56.3° and the circuit is inductive.
Hint
First, calculate the inductive and capacitive reactances. Compare them to determine the circuit type. Then use the formula for the phase angle: φ = arctan((X_L - X_C) / R).