What is the power factor in a circuit with a resistance of 5 ohms and a reactanc

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Question: What is the power factor in a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

Options:

Correct Answer: √2/2

Exam Year: 2022

Solution:

Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.

What is the power factor in a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

What is the power factor in a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

Step 1: Identify the resistance (R) and reactance (X) in the circuit. Here, R = 5 ohms and X = 5 ohms.
Step 2: Calculate the impedance (Z) using the formula Z = √(R² + X²).
Step 3: Substitute the values into the formula: Z = √(5² + 5²).
Step 4: Calculate 5² + 5², which equals 25 + 25 = 50.
Step 5: Find the square root of 50: Z = √50.
Step 6: Now, calculate the power factor using the formula: Power factor = R/Z.
Step 7: Substitute R and Z into the power factor formula: Power factor = 5/√50.
Step 8: Simplify the fraction: Power factor = 5/√(25*2) = 5/(5√2) = 1/√2.
Step 9: To express it in a more common form, multiply the numerator and denominator by √2: Power factor = √2/2.

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