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AC Power
47 questions By Tony R. Kuphaldt
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Question 34 of 47
When a capacitor is to be connected in parallel with an inductive AC load to correct for lagging power factor, it is important to be able to calculate the reactive power of the capacitor (QC). Write at least one equation for calculating the reactive power of a capacitor (in VARs) given the capacitor’s reactance (XC) at the line frequency.
Reveal answer$${Q}_{C} = \frac{E^2}{X_C} \ \ \ \ \ \ \ {Q}_{C} = I^2{{X}_{C}}$$
Follow-up question: which of the two equations shown above would be easiest to use in calculating the reactive power of a capacitor given the following information?
Notes:This step seems to be one of the most difficult for students to grasp as they begin to learn to correct for power factor in AC circuits, so I wrote a question specifically focusing on it. Once students calculate the amount of reactive power consumed by the load (Qload), they may realize the capacitor needs to produce the same (QC), but they often become mired in confusion trying to take the next step(s) in determining capacitor size.
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Question 35 of 47
An inductive AC load draws 13.4 amps of current at a voltage of 208 volts. The phase shift between line voltage and line current is measured with an oscilloscope, and determined to be 23o. Calculate the following:
- Apparent power (S) =
- True power (P) =
- Reactive power (Q) =
- Power factor =
An electrician suggests to you that the lagging power factor may be corrected by connecting a capacitor in parallel with this load. If the capacitor is sized just right, it will exactly offset the reactive power of the inductive load, resulting in zero total reactive power and a power factor of unity (1). Calculate the size of the necessary capacitor in Farads, assuming a line frequency of 60 Hz.
Reveal answer- Apparent power (S) = 2.787 kVA
- True power (P) = 2.567 kW
- Reactive power (Q) = 1.089 kVAR
- Power factor = 0.921
- Correction capacitor value = 66.77 μF
Challenge question: write an equation solving for the power factor correction capacitor size (in Farads) given any or all of the variables provided in the question (S, P, Q, f, V, P.F.).
Notes:There are multiple methods of solution for this problem, so be sure to have your students present their thoughts and strategies during discussion! The formula they write in answer to the challenge question will be nothing more than a formalized version of the solution strategy.
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Question 36 of 47
An AC load exhibits a lagging power factor of 0.73 at 230 VAC and 315 amps. If the system frequency is 60 Hz, calculate the following:
- Apparent power (S) =
- True power (P) =
- Reactive power (Q) =
- Θ =
- Necessary parallel C size to correct power factor to unity =
Reveal answer- Apparent power (S) = 72.45 kVA
- True power (P) = 52.89 kW
- Reactive power (Q) = 49.52 kVAR
- Θ = 43.11o
- Necessary parallel C size to correct power factor to unity = 2,483 μF
Notes:There are multiple methods of solution for this problem, so be sure to have your students present their thoughts and strategies during discussion!
