What is the power triangle equation?

What is the power triangle equation?

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

Answer: (B)

The power triangle equation describes the relationship between three key quantities in AC electrical circuits: active power (P), reactive power (Q), and apparent power (S). In this context, the power triangle is represented as: S^2 = P^2 + Q^2 Here, S represents the apparent power, which is measured in volt-amperes (VA), and it is the vector sum of the active power and reactive power. Active power (P), measured in watts (W), represents the actual power consumed by the circuit to perform useful work, while reactive power (Q), measured in reactive volt-amperes (VAR), accounts for the energy that oscillates between the source and the reactive components in the system (like inductors and capacitors). This relationship showcases that the apparent power is the hypotenuse of a right triangle where the active power and reactive power represent the two other sides. Understanding this triangle helps in analyzing power systems and ensuring efficient power usage, providing insight into how much real power is being used versus the total power supplied by the system. The formulation is critical in electrical engineering, especially when selecting equipment, conducting power quality assessments, or designing compensation systems.

The power triangle equation describes the relationship between three key quantities in AC electrical circuits: active power (P), reactive power (Q), and apparent power (S). In this context, the power triangle is represented as:

S^2 = P^2 + Q^2

Here, S represents the apparent power, which is measured in volt-amperes (VA), and it is the vector sum of the active power and reactive power. Active power (P), measured in watts (W), represents the actual power consumed by the circuit to perform useful work, while reactive power (Q), measured in reactive volt-amperes (VAR), accounts for the energy that oscillates between the source and the reactive components in the system (like inductors and capacitors).

This relationship showcases that the apparent power is the hypotenuse of a right triangle where the active power and reactive power represent the two other sides. Understanding this triangle helps in analyzing power systems and ensuring efficient power usage, providing insight into how much real power is being used versus the total power supplied by the system.

The formulation is critical in electrical engineering, especially when selecting equipment, conducting power quality assessments, or designing compensation systems.