Capacitor needed for phase angle change (RLC network)

AI Thread Summary
To improve the power factor of an inductive load from 0.81 to 0.96, a capacitor must be added to the circuit. The calculations involve determining the apparent power (S) and reactive power (Q) using the formulas provided. The user consistently arrives at a capacitance of 271uF, while the professor suggests the correct value is 398.17uF. Clarification on the calculation process and potential errors in the user's approach is sought. Accurate calculations are essential for achieving the desired power factor improvement.
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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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