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 = 38 kWQ = 31.5 kvarS = ?φ

A load takes 38 kW of real power and 31.5 kvar of reactive power (lagging). Find the apparent power S.

P = 38 kWQ = 31.5 kvar
S = kVA
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 4 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 240 VI = 4 Apf = cos φ = 0.85
P = W
3.Medium
P = 5 kWQ = ?Sφ

A single-phase motor takes 5 kW at a power factor of 0.6 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 5 kWpf = 0.6V = 400 V
Q = kvar
4.Medium
400 V115 kW, 0.85225 kW, 0.8I

Two loads are connected in parallel to a 400 V single-phase supply: a 15 kW load at a power factor of 0.85 lagging and a 25 kW load at a power factor of 0.8 leading. Find the overall power factor cos φ seen by the supply.

V = 400 VP1 = 15 kW, pf1 = 0.85 laggingP2 = 25 kW, pf2 = 0.8 leading
cos φ =
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 20 kWpf1 = 0.7pf2 = 0.9V = 400 Vf = 50 Hz
C = µF
6.Hard
230 V50 Hzload29 kW, 0.8C150 µFI

A single-phase load takes 29 kW at a power factor of 0.8 lagging from a 230 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 = 29 kWpf1 = 0.8V = 230 Vf = 50 HzC = 150 µF
cos φ =

Answer key

  1. 1. S = 49.36 kVA
  2. 2. P = 816 W
  3. 3. Q = 6.667 kvar
  4. 4. cos φ = 0.9732
  5. 5. C = 213.2 µF
  6. 6. cos φ = 0.8331

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