Calculating Reactive Power in an AC System

The question asks for the reactive power of a system given the voltage, current, and the phase angle between them. Reactive power is a key component of AC power systems and is measured in Volt-Ampere Reactive (VAR).

Understanding the Given Parameters

We are provided with the following information:

• Voltage (V): 230 V AC
• Current (I): 5 A
• Phase lag: 30° (This is the power factor angle, \(\phi\))

A lagging phase angle typically indicates an inductive load.

Formula for Reactive Power

In an AC circuit, the reactive power (Q) is calculated using the formula:

\[Q = V \times I \times \sin(\phi)\]

Where:

• \(Q\) is the reactive power in VAR
• \(V\) is the RMS voltage in Volts
• \(I\) is the RMS current in Amperes
• \(\phi\) is the phase angle between the voltage and current

Step-by-Step Calculation of Reactive Power

Using the given values, we can substitute them into the formula:

Given: \(V = 230\,V\), \(I = 5\,A\), \(\phi = 30^\circ\)

First, find the sine of the phase angle:

\[\sin(30^\circ) = 0.5\]

Now, plug the values into the reactive power formula:

\[Q = 230\,V \times 5\,A \times \sin(30^\circ)\]

\[Q = 230 \times 5 \times 0.5\]

\[Q = 1150 \times 0.5\]

\[Q = 575\]

The reactive power is 575 VAR.

Interpreting the Result

The calculated reactive power is 575 VAR. Reactive power is associated with the energy stored and returned by reactive components like inductors and capacitors. In a lagging power factor scenario (as indicated by the lag of 30°), the reactive power is inductive.

Comparison with Options

Let's compare our calculated value with the given options:

Our calculated value of 575 VAR matches Option 4.

Reactive Power Definition and Significance

Reactive power is the portion of AC power that does not result in useful work. It flows back and forth between the source and the load. Inductive loads (like motors and transformers) consume lagging reactive power, while capacitive loads (like capacitors) supply leading reactive power. Managing reactive power is important for maintaining voltage stability and efficiency in power transmission and distribution systems.

Revision Table: AC Power Concepts

Additional Information: The Power Triangle

The relationship between apparent power (S), real power (P), and reactive power (Q) can be visualized using the power triangle. It's a right-angled triangle where:

• The hypotenuse represents the apparent power (S).
• The adjacent side (usually horizontal) represents the real power (P).
• The opposite side (usually vertical) represents the reactive power (Q).

The Pythagorean relationship holds:

\[S^2 = P^2 + Q^2\]

The angle between apparent power (S) and real power (P) is the power factor angle (\(\phi\)).

• For lagging power factor (inductive loads), Q is positive and plotted upwards.
• For leading power factor (capacitive loads), Q is negative and plotted downwards.

Understanding the power triangle helps in analyzing and improving the power factor of electrical systems.