Capacitor needed for phase angle change (RLC network)

In summary, the conversation discusses the need to improve the power factor of an inductive load connected to a 120V (rms), 60Hz AC source. The load currently draws 5.0 kW at a power factor of 0.81 (lagging) and needs to be improved to 0.96 (lagging) by adding a capacitor. The necessary capacitance, in uF, is determined using the equations P/|S| = cos(phi), Q = V^2/X, and S = sqrt(P^2 + Q^2). The correct answer, according to the professor, is 398.17uF, while the student's solution is 271uF.
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Homework Statement


An inductive load is connected to a 120V (rms), 60Hz AC source. The load draws 5.0 kW at a power factor of 0.81 (lagging). You need to improve your power factor to 0.96 (lagging) by adding a capacitor.

What is the Capacitance needed (in uF)?

Homework Equations


P/|S| = cos(phi)
Q = V^2/X
S = sqrt(P^2 + Q^2)

The Attempt at a Solution


Please see photo with my solution attached. My professor says the answer is actually 398.17uF. I did this problem multiple times and never got that answer. I keep getting what I got in the photo attached (271uF).
 

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  • #2
It's hard to make out your work in that sideways photo. Can you explain your approach?
 

1. What is a capacitor and how does it affect phase angle change in an RLC network?

A capacitor is an electronic component that stores electrical energy in the form of an electric charge. In an RLC network, a capacitor can change the phase angle between the voltage and current by storing and releasing energy based on the frequency of the applied voltage. This results in a phase shift between the voltage and current, which can be used to control the power factor in an AC circuit.

2. How do I calculate the value of capacitor needed to achieve a desired phase angle change in an RLC network?

The value of the capacitor needed to achieve a certain phase angle change in an RLC network can be calculated using the formula C = (1/2πfR) * tan(θ), where C is the capacitance in Farads, f is the frequency in Hertz, R is the resistance in Ohms, and θ is the desired phase angle change in degrees.

3. Can a capacitor be used to change the phase angle in a DC circuit?

No, a capacitor cannot change the phase angle in a DC circuit as it only affects the phase angle in an AC circuit. In a DC circuit, the voltage and current are always in phase with each other.

4. What are the other factors that can affect the phase angle change in an RLC network besides the capacitor?

Besides the capacitor, the other factors that can affect the phase angle change in an RLC network are the frequency of the applied voltage, the resistance of the circuit, and the inductance of the inductor. The frequency and resistance can be adjusted to change the phase angle, while the inductance can also affect the phase angle due to the phenomenon of inductive reactance.

5. How does a capacitor help in improving the power factor in an AC circuit?

A capacitor can help improve the power factor in an AC circuit by reducing the reactive power and increasing the active power. This is because the capacitor stores and releases energy to help balance out the reactive power caused by the inductive load in the circuit, resulting in a higher power factor and more efficient energy usage.

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