Question

Find the complex power, the average power, and the reactive power for a circuit with:

v(t) = 112 cos(ωt + 10∘ ) V
i(t) = 4 cos(ωt - 50∘ )

Answer 1

To find complex power, average power, and reactive power in an AC circuit, use the RMS values of voltage and current, and factor in the phase difference between voltage and current using trigonometric functions.

Step-by-step explanation:

The question requires calculating the complex power, the average power, and the reactive power of an AC circuit given the voltage and current equations. Complex power (S) is the product of the RMS voltage and the conjugate of the RMS current. The average power (P) is the real part of the complex power, and the reactive power (Q) is the imaginary part of the complex power.

First, we find the RMS values of the voltage (Vrms) and current (Irms). The RMS value is the peak value divided by the square root of 2. Thus, Vrms = 112 V / √2 and Irms = 4 A / √2. Then, we calculate the complex power using S = Vrms * Irms * e^(jθ), where θ is the phase difference between voltage and current. In this case, θ = 10° - (-50°) = 60°.

To get the average power, we use P = Vrms * Irms * cos(θ). And for reactive power, the formula is Q = Vrms * Irms * sin(θ). Plugging in the phase angle into the appropriate trigonometric functions will yield the necessary power values.