For the circuit in Figure 15-61, find the true power, the reactive power, and the apparent power.

Question

Accepted Answer

The capacitive reactance and currents through R and C are

[latex]X_{C}= \frac{1}{2\pi fC} = \frac{1}{2\pi (1000 \ Hz)(0.15 \ \mu F)}= 1061 \ \Omega [/latex]

[latex]I_{R}= \frac{V_{s}}{R}= \frac{10 \ V}{470 \ \Omega }= 21.3 \ mA[/latex]

[latex]I_{C}= \frac{V_{s}}{X_{C}}= \frac{10 \ V}{1061 \ \Omega }= 9.43 \ mA[/latex]

The true power is

[latex]P_{true}[/latex] = [latex]I^{2}_{R}R[/latex] = [latex](21.3 mA)^{2}[/latex] (470 Ω) = 213 mW

The reactive power is

[latex]P_{r}[/latex]= [latex]I^{2}_{C}X_{C}[/latex]= [latex](9.43 mA)^{2}[/latex] (1061 Ω)= 94.3 mVAR

The apparent power is

[latex]P_{a}= \sqrt{P^{2}_{true} + P^{2}_{r}} = \sqrt{(213 \ mW)^{2}+ (94.3 \ mVAR)^{2}}= 233 \ mVA [/latex]

Question 15.24: For the circuit in Figure 15-61, find the true power, the re...