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PHY 102 Test Compilation PHY 102 10 Objective Question
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Question

An inductor, L = 0.5H, in series with a resistor, R = 250Ω, are connected to an a.c. source 100v, 50Hz. Determine the power factor of the circuit.
Options
A 0.84
B 0.85
Correct Answer
C 1.00
D 0.90
Correct Answer

Option B is the correct answer.

Detailed Explanation

Given:Resistance (R) = 250 ΩInductance (L) = 0.5 HFrequency (f) = 50 Hz1. Calculate the angular frequency (ω):ω = 2πf = 2π(50 Hz) = 100π rad/s2. Calculate the inductive reactance (XL):XL = ωL = 100π rad/s × 0.5 H = 50π Ω ≈ 157.08 Ω3. Calculate the impedance (Z) of the R-L series circuit:Z = √(R2 + XL2) = √(2502 + (50π)2)Z = √(62500 + 24674.01) = √(87174.01) ≈ 295.25 Ω4. Calculate the power factor (cos φ):The power factor is the ratio of resistance to impedance: cos φ = R/Zcos φ = 250 Ω / 295.25 Ω ≈ 0.8467Rounding to two decimal places, the power factor is approximately 0.85.

Hint

The power factor in an R-L series AC circuit is given by cos φ = R/Z. First, calculate the inductive reactance (XL) and then the total impedance (Z).

Question Info

Course: PHY 102
Topic: Test Compilation PHY 102 10
Type: Objective
Difficulty: Not specified
Question 894 of 1819
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