What is the power factor of a circuit with a resistance of 30Ω and a reactance o

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Question: What is the power factor of a circuit with a resistance of 30Ω and a reactance of 40Ω? (2023)

Options:

Correct Answer: 0.6

Exam Year: 2023

Solution:

Power factor = R/Z where Z = √(R² + X²). Calculate.

What is the power factor of a circuit with a resistance of 30Ω and a reactance of 40Ω? (2023)

What is the power factor of a circuit with a resistance of 30Ω and a reactance of 40Ω? (2023)

Step 1: Identify the resistance (R) and reactance (X) values. Here, R = 30Ω and X = 40Ω.
Step 2: Calculate the impedance (Z) using the formula Z = √(R² + X²).
Step 3: Substitute the values into the formula: Z = √(30² + 40²).
Step 4: Calculate 30² = 900 and 40² = 1600. Then, add them: 900 + 1600 = 2500.
Step 5: Find the square root of 2500: Z = √2500 = 50Ω.
Step 6: Now, calculate the power factor using the formula: Power factor = R/Z.
Step 7: Substitute the values: Power factor = 30Ω / 50Ω.
Step 8: Simplify the fraction: Power factor = 0.6.

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