A three-phase generator delivers current at a power factor of 75% with a terminal voltage of 480 V and a full load current of 300 A. What is the apparent power?

A three-phase generator delivers current at a power factor of 75% with a terminal voltage of 480 V and a full load current of 300 A. What is the apparent power?

• A. 249.12 kVA
• B. 300 kVA
• C. 250 kVA
• D. 220 kVA

Answer: (A)

To determine the apparent power delivered by the three-phase generator, we can use the formula for apparent power in a three-phase system, which is given by: \[ S = \sqrt{3} \times V_L \times I \] Where: - \( S \) is the apparent power in VA (or kVA when divided by 1000), - \( V_L \) is the line-to-line voltage in volts, - \( I \) is the current in amperes. In this situation, the terminal voltage is provided as 480 V, and the full load current is 300 A. Plugging these values into the formula gives: \[ S = \sqrt{3} \times 480 \, V \times 300 \, A \] Calculating this step-by-step: 1. Calculate \( \sqrt{3} \): Approximately \( 1.732 \). 2. Multiply \( 1.732 \) by \( 480 \): \[ 1.732 \times 480 \approx 829.76 \, V \] 3. Now, multiply this result by \( 300 \): \[ 829.76 \

To determine the apparent power delivered by the three-phase generator, we can use the formula for apparent power in a three-phase system, which is given by:

[

S = \sqrt{3} \times V_L \times I

]

Where:

• ( S ) is the apparent power in VA (or kVA when divided by 1000),

• ( V_L ) is the line-to-line voltage in volts,

• ( I ) is the current in amperes.

In this situation, the terminal voltage is provided as 480 V, and the full load current is 300 A. Plugging these values into the formula gives:

[

S = \sqrt{3} \times 480 , V \times 300 , A

]

Calculating this step-by-step:

1. Calculate ( \sqrt{3} ): Approximately ( 1.732 ).

2. Multiply ( 1.732 ) by ( 480 ):

[

1.732 \times 480 \approx 829.76 , V

]

3. Now, multiply this result by ( 300 ):

[

829.76 \