Final answer:
The active, apparent, and reactive power in an AC circuit relate to the rms values of current and voltage and the phase angle between them. A power diagram can visualize these concepts. A capacitor can be added in parallel to improve the power factor, with its value calculated based on circuit parameters
Step-by-step explanation:
Calculating Power in an AC Circuit
The question relates to the calculation and understanding of active, apparent, and reactive power in an alternating current (AC) circuit, and how to modify the circuit to improve its power factor. To calculate these values, first recall that the average power (Pave) in an AC circuit is given by Pave = Irms * Vrms * cos(φ), where Irms is the root mean square current, Vrms is the root mean square voltage, and cos(φ) is the power factor which is the cosine of the phase angle between the current and voltage.
To find the apparent power (S), which has units of volt-amperes (VA), use the formula S = Irms * Vrms. The reactive power (Q), measured in reactive volt-amperes (VAR), can be calculated using Q = Irms * Vrms * sin(φ), where sin(φ) is the sine of the phase angle. Active power (P), measured in watts (W), is what is given by the first equation, Pave.
A power diagram or power triangle can be drawn to visually represent the relationship between these forms of power. The apparent power forms the hypotenuse, with active power on the adjacent side and reactive power on the opposite side to the angle representing the current phase angle.
To increase the power factor to 0.95, you can add a capacitor in parallel to the circuit. The formula 2π√LC is relevant for calculating resonant frequency, and adding a capacitor will reduce the overall reactance, hence adjusting the phase angle and the power factor. The exact value of the required capacitance would depend on the circuit parameters which are not provided in this scenario.