If the reactive power of a three-phase system is 12 kVAR and the active power is 16 kW, then what is the apparent power?

Explanation:

Apparent Power Calculation in a Three-Phase System:

Definition: Apparent power is the total power flowing in an electrical circuit and is a combination of both active power (real power) and reactive power. It is measured in volt-amperes (VA) or kilovolt-amperes (kVA). Apparent power represents the vector sum of active power and reactive power in a circuit.

Formula: The relationship between apparent power (S), active power (P), and reactive power (Q) in an electrical circuit is given by the equation:

S = √(P² + Q²)

Where:

• S = Apparent Power (in kVA)
• P = Active Power (in kW)
• Q = Reactive Power (in kVAR)

Given Data:

• Reactive Power (Q) = 12 kVAR
• Active Power (P) = 16 kW

Step-by-Step Solution:

1. Substitute the values of active power (P) and reactive power (Q) into the formula for apparent power:

S = √(P² + Q²)

2. Calculate the squares of active power and reactive power:

P² = (16 kW)² = 256 kW²

Q² = (12 kVAR)² = 144 kVAR²

3. Add the squared values:

P² + Q² = 256 + 144 = 400

4. Find the square root of the sum to calculate the apparent power:

S = √400 = 20 kVA

Correct Answer:

The apparent power of the three-phase system is 20 kVA. Hence, the correct option is:

Option 1: 20 kVA

Additional Information

Analysis of Other Options:

To understand why the other options are incorrect, let’s analyze them:

Option 2: 28 kVA

This value is incorrect because it does not match the calculation based on the formula for apparent power. If we substitute the given values of active and reactive power into the formula, the result is clearly 20 kVA, not 28 kVA. This option might arise from a misunderstanding of the formula or incorrect calculations.

Option 3: 4 kVA

This value is far below the calculated apparent power and does not correspond to the given active and reactive power values. It could be derived from an erroneous assumption or misinterpretation of the relationship between active power, reactive power, and apparent power.

Option 4: 10 kVA

While this value is closer to the actual apparent power, it is still incorrect. The apparent power must be calculated using the formula √(P² + Q²), which yields 20 kVA for the given values of active and reactive power. This option might result from halving or incorrectly approximating the calculated apparent power.

Conclusion:

The correct calculation of apparent power, based on the formula and the given values of active and reactive power, leads to a result of 20 kVA. Understanding the relationship between active power, reactive power, and apparent power is essential for accurate calculations in electrical systems. This ensures that the correct option is chosen, and incorrect options are identified as arising from calculation errors or misunderstandings of the formula.