Question Detail
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.
Correct Answer
Option B is the correct answer.
Detailed Explanation
Given:
Inductance (L) = 0.5 H
Resistance (R) = 250 Ω
Frequency (f) = 50 Hz
First, calculate the angular frequency (ω):
ω = 2πf = 2π * 50 = 100π rad/s
Next, calculate the inductive reactance (XL):
XL = ωL = 100π * 0.5 = 50π Ω ≈ 157.08 Ω
Now, calculate the impedance (Z) of the R-L series circuit:
Z = √(R2 + XL2)
Z = √(2502 + (50π)2)
Z = √(62500 + 24674.01)
Z = √(87174.01) ≈ 295.25 Ω
Finally, calculate the power factor (cos φ):
Power Factor = R / Z
Power Factor = 250 Ω / 295.25 Ω ≈ 0.8467
Rounding to two decimal places, the power factor is 0.85.
Hint
The power factor of an AC circuit is given by cos φ = R/Z, where R is the resistance and Z is the impedance. For an R-L series circuit, Z = √(R2 + XL2), and XL = ωL.