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 = ?QS = V·Iφ

A single-phase load draws 14 A (rms) from a 230 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 230 VI = 14 Apf = cos φ = 0.75
P = W
2.Easy
P = 31.5 kWQ = 38 kvarS = ?φ

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

P = 31.5 kWQ = 38 kvar
S = kVA
3.Medium
P = 29 kWQSφ

A single-phase motor takes 29 kW at a power factor of 0.9 lagging from a 240 V supply. Find the line current I.

P = 29 kWpf = 0.9V = 240 V
I = A
4.Medium
P = 8 kWQSφ

A single-phase motor takes 8 kW at a power factor of 0.6 lagging from a 400 V supply. Find the line current I.

P = 8 kWpf = 0.6V = 400 V
I = A
5.Hard
240 V50 Hzload24 kW, 0.8C220 µFI

A single-phase load takes 24 kW at a power factor of 0.8 lagging from a 240 V, 50 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 24 kWpf1 = 0.8V = 240 Vf = 50 HzC = 220 µF
cos φ =
6.Hard
P1​ = 42 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 42 kW at a power factor of 0.8 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 150 kVAP1 = 42 kWpf1 = 0.8
ΔP = kW

Answer key

  1. 1. P = 2415 W
  2. 2. S = 49.36 kVA
  3. 3. I = 134.3 A
  4. 4. I = 33.33 A
  5. 5. cos φ = 0.8635
  6. 6. ΔP = 104.7 kW

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