Question

Required informetion Consider the following values Find the complex power, the average power, and the reactlve power. τ(t)=100cos(ωt+10*)V and i(t)=4cos(ωt−50*)A

The cortiplek power is: (_____)/(_____))VA.
The average power is ____ W
The reactive power is ____ VAR

Answer 1

The complex power is calculated using the rms values of voltage and current, and the cosine and sine of the phase angle. The average power is the real part of the complex power, and the reactive power is the imaginary part.

Step-by-step explanation:

To find the complex power, we use the formula S = Vrms * Irms * (cosφ + j sinφ), where Vrms and Irms are the root mean square values of voltage and current, respectively, and φ is the phase angle between them. The average power, also known as real power, is given by P = Vrms * Irms * cosφ, and the reactive power is Q = Vrms * Irms * sinφ.

First, we need to convert the peak values of voltage and current to their respective rms values: Vrms = Vpeak / √2 and Irms = Ipeak / √2. The voltage and current equations can be rewritten as τ(t) = Vpeak * cos(ωt + 10°) and i(t) = Ipeak * cos(ωt - 50°). This implies that Vpeak = 100V and Ipeak = 4A, so Vrms = 100V / √2 and Irms = 4A / √2.

The phase difference φ is found by subtracting the voltage phase angle from the current phase angle: φ = -50° - (+10°) = -60°. We plug these values into the formulas to calculate the complex power, average power, and reactive power.

Thus, the complex power is: (Vrms * Irms * cosφ) / (Vrms * Irms * sinφ) VA, the average power is Vrms * Irms * cosφ W, and the reactive power is Vrms * Irms * sinφ VAR.