Question

The vector sum of

• A. Real Power and Reactive Power is Apparent Power
• B. Real Power and Apparent Power is Reactive Power
• C. Apparent Power and Reactive Power is Real Power
• D. Real Power, Reactive Power and Apparent Power is always zero.

Hint:

To remember this relationship, visualize the standard right-angled triangle where:
\[ \text{Real Power (Base)} + j \cdot \text{Reactive Power (Height)} = \text{Apparent Power (Hypotenuse)} \] This visual reference makes calculating any of the three values straightforward.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In AC circuits, the power consumed by a load is represented in a complex plane. This complex power consists of two orthogonal components: real power (which does useful work) and reactive power (which maintains magnetic/electric fields).
Key Formula or Approach:
These power terms are geometrically represented using a right-angled triangle called thePower Triangle, where:
The horizontal leg represents Real Power (\(P\)), measured in Watts (\(\text{W}\)).

The vertical leg represents Reactive Power (\(Q\)), measured in Volt-Amperes Reactive (\(\text{VAR}\)).

The hypotenuse represents Apparent Power (\(S\)), measured in Volt-Amperes (\(\text{VA}\)).
In vector notation: \[ \vec{S} = P + jQ \]

Step 2: Detailed Explanation:
Since Real Power (\(P\)) and Reactive Power (\(Q\)) act along perpendicular axes in the complex power plane, their combined effect is their vector sum.
The magnitude of this vector sum is given by the Pythagorean relation: \[ S = |\vec{S}| = \sqrt{P^2 + Q^2} \] This hypotenuse represents the Apparent Power (\(S\)), which is the total power that the utility system must generate and transmit to the load.
Let us review the incorrect options:
- Option (B) is incorrect because reactive power is the vector difference: \(Q = \sqrt{S^2 - P^2}\).
- Option (C) is incorrect because real power is the vector difference: \(P = \sqrt{S^2 - Q^2}\).
- Option (D) is physically incorrect as these three quantities do not sum to zero.

Step 3: Final Answer:
The vector sum of Real Power and Reactive Power is Apparent Power, which corresponds to Option (A).