Understanding Power Factor Calculation

This question asks us to find the power factor (PF) of a three-phase motor given the real power it draws and the apparent power supplied to it.

Key Concepts

• Real Power (P): This is the actual power consumed by the motor to perform useful work. It's measured in Watts (W) or Kilowatts (kW). In this problem, P = 5.6 kW.
• Apparent Power (S): This is the total power supplied to the circuit, which is the product of the voltage and current. It's measured in Volt-Amperes (VA) or Kilo Volt-Amperes (kVA). In this problem, S = 7000 VA.
• Power Factor (PF): This is the ratio of real power to apparent power. It represents the efficiency of the electrical system in converting supplied power into useful work. It is a dimensionless quantity between 0 and 1.

Formula for Power Factor

The relationship between real power, apparent power, and power factor is given by the formula:

$$ P = S \times PF $$

To find the power factor, we can rearrange the formula:

$$ PF = \frac{P}{S} $$

Step-by-Step Calculation

1. Convert Units: First, ensure both power values are in the same units. The real power is given in kilowatts (kW), and the apparent power is in Volt-Amperes (VA). Let's convert the real power from kW to VA.
   Real Power (P) = 5.6 kW = 5.6 $\times$ 1000 VA = 5600 VA.
2. Apply the Formula: Now, substitute the values of P and S into the power factor formula:
   $$ PF = \frac{\text{Real Power (P)}}{\text{Apparent Power (S)}} $$
   $$ PF = \frac{5600 \text{ VA}}{7000 \text{ VA}} $$
3. Calculate the Result: Perform the division:
   $$ PF = \frac{56}{70} $$
   $$ PF = \frac{56 \div 14}{70 \div 14} $$
   $$ PF = \frac{4}{5} $$
   $$ PF = 0.8 $$

Conclusion

The calculated power factor for the three-phase motor is 0.8. This value indicates that the motor is utilizing 80% of the supplied apparent power to perform useful work.