What is the relationship between reactive power and apparent power in a circuit?

The correct relationship between reactive power and apparent power in an alternating current (AC) circuit is represented by the geometrical analogy of a right triangle. In this triangle, the three relevant quantities are active power (real power), reactive power, and apparent power.

Apparent power, denoted as S, is the combination of both active power (P) and reactive power (Q). The relationship can be visually represented using the formula:

[ S = \sqrt{P^2 + Q^2} ]

In this context, active power is located on one side of the triangle (adjacent), reactive power is on the other (opposite), and the hypotenuse represents the apparent power. This right triangle reflects the fundamental relationship among these quantities, as the theorem expresses how they are interconnected: the square of the apparent power is equal to the sum of the squares of active and reactive power.

Understanding this right triangle relationship is essential in electrical engineering, especially when analyzing power in AC circuits, since it helps to visualize how reactive power and active power contribute to the total power flowing in a system.