Motor Active Power Calculation Explained

Understanding the power consumed by an AC motor involves knowing the relationship between different types of power: apparent power, active power, and reactive power. These are linked together by the power factor.

What are Apparent Power, Active Power, and Power Factor?

• Apparent Power (S): This is the total power supplied to a circuit. It is the product of the RMS voltage and the RMS current. Its unit is Volt-Ampere (VA). It represents the total power "seen" by the source.
• Active Power (P): This is the actual power consumed by the load and converted into useful work (like mechanical energy in a motor). Its unit is Watt (W). This is the power that performs work.
• Power Factor (PF): This is a measure of how effectively the apparent power is being converted into active power. It is defined as the ratio of active power to apparent power. Mathematically, $PF = \frac{P}{S}$. It is a dimensionless quantity and ranges from 0 to 1 (or 0% to 100%). For sinusoidal circuits, it is also equal to the cosine of the phase angle ($\theta$) between the voltage and current: $PF = \cos(\theta)$.

Calculating Active Power

The formula connecting active power (P), apparent power (S), and power factor (PF) is derived from the definition of power factor:

$$P = S \times PF$$

In this question, we are given the following values for the motor:

• Total power (Apparent Power, S) = 400 VA
• Power factor (PF) = 0.5

We need to calculate the active power (P) consumed by the motor.

Step-by-Step Calculation

Using the formula $P = S \times PF$, we substitute the given values:

$$P = 400 \, \text{VA} \times 0.5$$

Now, perform the multiplication:

$$P = 200 \, \text{W}$$

So, the active power consumed by the motor is 200 Watts.

Summary of Calculation

The calculation shows that when the apparent power is 400 VA and the power factor is 0.5, the active power consumed is 200 W. This means that out of the total 400 VA supplied, only 200 W is actually converted into useful work by the motor, with the remaining power being reactive power.