Question Detail
Question
A given RLC circuit has R=100Ω, L=1H and C=10µF all connected in series with a source of 200sinωt 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: R = 100 Ω, L = 1 H, C = 10 µF = 10 x 10-6 F, ω = 400 rad/s. 1. Calculate inductive reactance (XL): XL = ωL = 400 rad/s * 1 H = 400 Ω. 2. Calculate capacitive reactance (XC): XC = 1/(ωC) = 1/(400 rad/s * 10 x 10-6 F) = 1/(4 x 10-3) = 1000/4 = 250 Ω. 3. Calculate the phase angle (φ): tan(φ) = (XL - XC) / R = (400 Ω - 250 Ω) / 100 Ω = 150 Ω / 100 Ω = 1.5. φ = arctan(1.5) ≈ 56.31°. 4. Determine the circuit type: Since XL (400 Ω) > XC (250 Ω), the circuit is inductive. Therefore, the phase angle is approximately 56.3° and the circuit is inductive.
Hint
First, calculate the inductive and capacitive reactances. Then use these values along with the resistance to find the phase angle. The sign of (XL - XC) determines if the circuit is inductive or capacitive.