If the power factor of an AC circuit is 0.8, what is the angle between the curre

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Question: If the power factor of an AC circuit is 0.8, what is the angle between the current and voltage? (2021)

Options:

Correct Answer: 53.13°

Exam Year: 2021

Solution:

The angle θ can be found using cos(θ) = power factor. Thus, θ = cos⁻¹(0.8) ≈ 36.87°.

If the power factor of an AC circuit is 0.8, what is the angle between the current and voltage? (2021)

If the power factor of an AC circuit is 0.8, what is the angle between the current and voltage? (2021)

Step 1: Understand that the power factor is the cosine of the angle (θ) between the current and voltage in an AC circuit.
Step 2: Write the formula that relates the power factor to the angle: cos(θ) = power factor.
Step 3: Substitute the given power factor (0.8) into the formula: cos(θ) = 0.8.
Step 4: To find the angle θ, use the inverse cosine function: θ = cos⁻¹(0.8).
Step 5: Use a calculator to compute cos⁻¹(0.8), which gives approximately 36.87°.

Power Factor – The power factor is the cosine of the phase angle between the current and voltage in an AC circuit, indicating the efficiency of power usage.
Trigonometric Functions – Understanding how to use inverse trigonometric functions to find angles from cosine values.