In an AC circuit, if the power factor is 0.5, what is the angle φ between the vo

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Question: In an AC circuit, if the power factor is 0.5, what is the angle φ between the voltage and current? (2019)

Options:

Correct Answer: 60 degrees

Exam Year: 2019

Solution:

The power factor (cosφ) is 0.5, which corresponds to an angle φ of 60 degrees.

In an AC circuit, if the power factor is 0.5, what is the angle φ between the voltage and current? (2019)

In an AC circuit, if the power factor is 0.5, what is the angle φ between the voltage and current? (2019)

Step 1: Understand that the power factor (PF) is defined as the cosine of the angle φ between the voltage and current in an AC circuit. This is written as PF = cos(φ).
Step 2: Given that the power factor is 0.5, we can write this as cos(φ) = 0.5.
Step 3: To find the angle φ, we need to determine which angle has a cosine value of 0.5.
Step 4: Recall that cos(60 degrees) = 0.5. Therefore, φ = 60 degrees.
Step 5: Conclude that the angle φ between the voltage and current is 60 degrees.

Power Factor – The power factor is the cosine of the phase angle (φ) between the voltage and current in an AC circuit, indicating the efficiency of power usage.
Phase Angle Calculation – Understanding how to calculate the phase angle from the power factor using the inverse cosine function.