In an AC circuit, if the current lags the voltage by 30 degrees, what is the pow

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Question: In an AC circuit, if the current lags the voltage by 30 degrees, what is the power factor? (2023)

Options:

Correct Answer: 0.866

Exam Year: 2023

Solution:

The power factor (PF) is given by cos(θ). If θ = 30 degrees, PF = cos(30°) = √3/2 ≈ 0.866.

In an AC circuit, if the current lags the voltage by 30 degrees, what is the power factor? (2023)

In an AC circuit, if the current lags the voltage by 30 degrees, what is the power factor? (2023)

Step 1: Understand that in an AC circuit, the current can either lead or lag the voltage. In this case, the current lags the voltage.
Step 2: Identify the angle by which the current lags the voltage. Here, it is given as 30 degrees.
Step 3: The power factor (PF) is calculated using the formula PF = cos(θ), where θ is the angle of lag.
Step 4: Substitute the angle into the formula. So, PF = cos(30°).
Step 5: Calculate cos(30°). The value of cos(30°) is √3/2.
Step 6: Convert √3/2 to a decimal for easier understanding. √3/2 is approximately 0.866.
Step 7: Conclude that the power factor is approximately 0.866.

Power Factor – The power factor in an AC circuit is the cosine of the phase angle (θ) between the current and voltage, indicating the efficiency of power usage.
Phase Angle – The phase angle represents the difference in timing between the voltage and current waveforms in an AC circuit.
Trigonometric Functions – Understanding how to apply trigonometric functions, specifically cosine, to calculate the power factor from the phase angle.