If a single-phase transformer circuit feeds a motor and lighting load of 50 kilowatts at a power factor of 0.8, what is the required kVA rating?

To determine the required kVA rating for a transformer feeding a motor and lighting load, you first need to understand the relationship between real power (in kW), apparent power (in kVA), and power factor. The formula that links these values is:

[

\text{kVA} = \frac{\text{kW}}{\text{Power Factor}}

]

In this scenario, the motor and lighting load is given as 50 kilowatts, and the power factor is 0.8.

Applying the formula:

[

\text{kVA} = \frac{50 \text{ kW}}{0.8} = 62.5 \text{ kVA}

]

This calculation shows that for a load of 50 kilowatts at a power factor of 0.8, the required apparent power (kVA) is 62.5. This is the amount of capacity the transformer must have to handle the real power demand while accounting for the inefficiency described by the power factor.

Using this analysis, the choice of 62.5 kVA is validated, ensuring that the transformer can safely and effectively provide for both the motor and lighting load without risk of overload or failure.