What is the imaginary power of a single-phase circuit with a real power of 3467 W and a power factor of 78.8%?

To determine the imaginary power in a single-phase circuit, you can use the relationship between real power (P), reactive power (Q), and apparent power (S). The power factor (PF) gives us an indication of how effectively the circuit is converting electrical power into useful work.

The power factor can be represented as the cosine of the phase angle (φ) between the current and voltage. Thus, you can find the apparent power (S) using the formula:

[ S = \frac{P}{\text{PF}} ]

Given that the real power (P) is 3467 W and the power factor is 78.8% (or 0.788), you can calculate the apparent power:

[ S = \frac{3467}{0.788} \approx 4400.76 \text{ VA} ]

Next, the apparent power can also be related to the real power and reactive power using the following formula:

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

From this, you can isolate the reactive power (Q):

[ Q = \sqrt{S^2 - P^2} ]

First, we can calculate ( P^2 ):

[ P^