Capacitor needed for phase angle change (RLC network)

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SUMMARY

The discussion centers on calculating the required capacitance to improve the power factor of an inductive load connected to a 120V (rms), 60Hz AC source. The load initially draws 5.0 kW at a power factor of 0.81 (lagging) and aims to achieve a power factor of 0.96 (lagging) by adding a capacitor. The correct capacitance value determined is 398.17 µF, contrasting with the user's repeated calculation of 271 µF. The discrepancy highlights the importance of accurately applying the equations for apparent power and reactive power in RLC networks.

PREREQUISITES
  • Understanding of RLC circuit theory
  • Familiarity with power factor concepts
  • Knowledge of AC circuit analysis
  • Proficiency in using the equations for apparent power (S), real power (P), and reactive power (Q)
NEXT STEPS
  • Review the calculation of reactive power (Q) in RLC circuits
  • Study the impact of capacitors on power factor correction
  • Learn about the relationship between power factor and energy efficiency in AC systems
  • Explore the use of power factor correction devices in industrial applications
USEFUL FOR

Electrical engineers, students studying AC circuit theory, and professionals involved in power factor correction and energy management will benefit from this discussion.

D.B0004
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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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It's hard to make out your work in that sideways photo. Can you explain your approach?
 

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