In a single-phase circuit, if the apparent power is 3000 VA and the real power is 2800 W, what is the power factor?

To find the power factor in a single-phase circuit, you can use the relationship between apparent power, real power, and power factor. The power factor (PF) is defined as the ratio of real power (measured in watts) to apparent power (measured in volt-amperes). The formula is:

[ \text{Power Factor} = \frac{\text{Real Power}}{\text{Apparent Power}} ]

In this case, you have the real power as 2800 W and the apparent power as 3000 VA. Plugging these values into the formula gives:

[ \text{Power Factor} = \frac{2800 , \text{W}}{3000 , \text{VA}} = \frac{28}{30} \approx 0.9333 ]

To express the power factor as a percentage, multiply by 100:

[ \text{Power Factor} \approx 93.33% ]

This confirms that the power factor is approximately 93.3%, which matches the given answer choice. This value also indicates a relatively efficient circuit, as power factors closer to 1 (or 100%) indicate less wasted power and a more effective use