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 = 50 kWQ = 27.5 kvarS = ?φ

A load takes 50 kW of real power and 27.5 kvar of reactive power (lagging). Find the apparent power S.

P = 50 kWQ = 27.5 kvar
S = kVA
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 19 A (rms) from a 120 V (rms) supply at a power factor of 0.95 lagging. Find the real power P it takes.

V = 120 VI = 19 Apf = cos φ = 0.95
P = W
3.Medium
P = 16 kWQ = ?Sφ

A single-phase motor takes 16 kW at a power factor of 0.9 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 16 kWpf = 0.9V = 400 V
Q = kvar
4.Medium
120 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 6 + j8 Ω
P = W
5.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 kW at a power factor of 0.65 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 35 kWpf1 = 0.65pf2 = 0.92V = 240 Vf = 50 Hz
C = µF
6.Hard
400 V50 Hzload25 kW, 0.7C150 µFI

A single-phase load takes 25 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A 150 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 25 kWpf1 = 0.7V = 400 Vf = 50 HzC = 150 µF
cos φ =

Answer key

  1. 1. S = 57.06 kVA
  2. 2. P = 2166 W
  3. 3. Q = 7.749 kvar
  4. 4. P = 864 W
  5. 5. C = 1437 µF
  6. 6. cos φ = 0.8121

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