AC power & power factor worksheet with answers

Free printable AC power & power factor worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 44.5 kWQ = 24.5 kvarS = ?φ

A load takes 44.5 kW of real power and 24.5 kvar of reactive power (lagging). Find the apparent power S.

P = 44.5 kWQ = 24.5 kvar
S = kVA
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 6 A (rms) from a 120 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 120 VI = 6 Apf = cos φ = 0.9
Q = var
3.Medium
120 VZ24 + j7 ΩI

A load with impedance Z = 24 + j7 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 24 + j7 Ω
P = W
4.Medium
240 VR + jXP = 2700 W12.5 A

An inductive load takes 12.5 A and 2700 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 12.5 AP = 2700 W
R = Ω
5.Hard
400 V60 Hzload15 kW, 0.8C22 µFI

A single-phase load takes 15 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A 22 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 15 kWpf1 = 0.8V = 400 Vf = 60 HzC = 22 µF
cos φ =
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.7 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 5 kWpf1 = 0.7pf2 = 0.92V = 240 Vf = 60 Hz
Inew = A

Answer key

  1. 1. S = 50.8 kVA
  2. 2. Q = 313.8 var
  3. 3. P = 553 W
  4. 4. R = 17.28 Ω
  5. 5. cos φ = 0.834
  6. 6. Inew = 22.64 A

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