Which of the following represents the relationship between apparent power, real power, and reactive power?

Which of the following represents the relationship between apparent power, real power, and reactive power?

• A. P = S + Q
• B. S = P + Q^2
• C. S^2 = P^2 + Q^2
• D. P = S - Q

Answer: (C)

The relationship between apparent power, real power, and reactive power is accurately represented by the equation where the square of the apparent power equals the sum of the squares of the real power and reactive power. In mathematical terms, this is often expressed as \( S^2 = P^2 + Q^2 \), where S is the apparent power, P is the real power, and Q is the reactive power. This equation arises from the geometric representation of power in AC circuits, often referred to as the power triangle. In this triangle, the real power (the horizontal side) represents the actual power consumed by the load, the reactive power (the vertical side) represents the power stored and released by the inductive and capacitive components, and the apparent power (the hypotenuse) is a combination of both real and reactive power. This fundamental relationship is key in understanding power flow in electrical systems and is critical for power factor analysis and improving energy efficiency in electrical engineering applications. Other options do not correctly represent the relationship between these types of power. For instance, stating that P equals S plus Q would suggest that real power is a sum of apparent and reactive power, which is not physically meaningful within the context of AC circuits.

The relationship between apparent power, real power, and reactive power is accurately represented by the equation where the square of the apparent power equals the sum of the squares of the real power and reactive power. In mathematical terms, this is often expressed as ( S^2 = P^2 + Q^2 ), where S is the apparent power, P is the real power, and Q is the reactive power.

This equation arises from the geometric representation of power in AC circuits, often referred to as the power triangle. In this triangle, the real power (the horizontal side) represents the actual power consumed by the load, the reactive power (the vertical side) represents the power stored and released by the inductive and capacitive components, and the apparent power (the hypotenuse) is a combination of both real and reactive power. This fundamental relationship is key in understanding power flow in electrical systems and is critical for power factor analysis and improving energy efficiency in electrical engineering applications.

Other options do not correctly represent the relationship between these types of power. For instance, stating that P equals S plus Q would suggest that real power is a sum of apparent and reactive power, which is not physically meaningful within the context of AC circuits.