What is the power factor of a circuit with a resistance of 5Ω and an inductive r

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Question: What is the power factor of a circuit with a resistance of 5Ω and an inductive reactance of 5Ω? (2022)

Options:

Correct Answer: 0.707

Exam Year: 2022

Solution:

Power factor = R/Z = 5 / √(5² + 5²) = 5 / √50 = 0.707.

What is the power factor of a circuit with a resistance of 5Ω and an inductive reactance of 5Ω? (2022)

What is the power factor of a circuit with a resistance of 5Ω and an inductive reactance of 5Ω? (2022)

Step 1: Identify the resistance (R) of the circuit, which is given as 5Ω.
Step 2: Identify the inductive reactance (X_L) of the circuit, which is also given as 5Ω.
Step 3: Calculate the impedance (Z) of the circuit using the formula Z = √(R² + X_L²).
Step 4: Substitute the values into the formula: Z = √(5² + 5²).
Step 5: Calculate 5², which is 25, and then add the two values: 25 + 25 = 50.
Step 6: Find the square root of 50: Z = √50.
Step 7: Now, calculate the power factor using the formula: Power factor = R/Z.
Step 8: Substitute the values: Power factor = 5 / √50.
Step 9: Simplify the expression to find the power factor: Power factor = 5 / 7.071 (approximately).
Step 10: The final value of the power factor is approximately 0.707.

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