For a 120VAC 60Hz circuit with a 10A load and a 20° lagging power factor, what is the true power consumption?

To determine the true power consumption in an AC circuit with a load, you can use the formula for real power (P), which incorporates the apparent power (S) and the power factor (PF):

[ P = S \times PF ]

First, we need to find the apparent power (S), which is calculated using the voltage and current:

[ S = V \times I ]

For this scenario:

• Voltage (V) = 120 V

• Current (I) = 10 A

Calculating apparent power:

[ S = 120 , \text{V} \times 10 , \text{A} = 1200 , \text{VA} ]

Next, the power factor (PF) accounts for the phase difference between the voltage and current in an AC circuit. The power factor is given as the cosine of the phase angle, which in this case is 20° lagging. Therefore, we calculate the power factor as follows:

[ PF = \cos(20°) \approx 0.9397 ]

Now, we can substitute the values into the formula for true power:

[ P = S \times PF = 1200 , \text{VA