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: R = 100 Ω, L = 1 H, C = 10 µF = 10 × 10-6 F, ω = 400 rad/s.First, calculate the inductive reactance XL and capacitive reactance XC:XL = ωL = 400 rad/s × 1 H = 400 Ω.XC = 1 / (ωC) = 1 / (400 rad/s × 10 × 10-6 F) = 1 / (0.004) Ω = 250 Ω.Since XL (400 Ω) > XC (250 Ω), the circuit is inductive.The phase angle φ is given by φ = arctan((XL - XC) / R).φ = arctan((400 Ω - 250 Ω) / 100 Ω) = arctan(150 Ω / 100 Ω) = arctan(1.5).φ ≈ 56.3°.Therefore, the phase angle is 56.3° and the circuit type is inductive.
Hint
Calculate the inductive and capacitive reactances. The circuit type is determined by which reactance is larger. The phase angle is found using the tangent of the ratio of net reactance to resistance.