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
PQ = ?S = V·Iφ

A single-phase load draws 10 A (rms) from a 400 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 400 VI = 10 Apf = cos φ = 0.65
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 16 A (rms) from a 400 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 400 VI = 16 Apf = cos φ = 0.6
Q = var
3.Medium
240 V113 kW, 0.6525 kW, 0.85I

Two loads are connected in parallel to a 240 V single-phase supply: a 13 kW load at a power factor of 0.65 lagging and a 5 kW load at a power factor of 0.85 lagging. Find the overall power factor cos φ seen by the supply.

V = 240 VP1 = 13 kW, pf1 = 0.65 laggingP2 = 5 kW, pf2 = 0.85 lagging
cos φ =
4.Medium
P = 28 kWQ = ?Sφ

A single-phase motor takes 28 kW at a power factor of 0.8 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 28 kWpf = 0.8V = 230 V
Q = kvar
5.Hard
P1​ = 30 kWQ1​S1​φ

A 75 kVA single-phase transformer supplies a load of 30 kW at a power factor of 0.65 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 = 75 kVAP1 = 30 kWpf1 = 0.65
ΔP = kW
6.Hard
P1​ = 27 kWQ1​S1​φ

A 100 kVA single-phase transformer supplies a load of 27 kW at a power factor of 0.75 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 = 100 kVAP1 = 27 kWpf1 = 0.75
ΔP = kW

Answer key

  1. 1. Q = 3040 var
  2. 2. Q = 5120 var
  3. 3. cos φ = 0.7013
  4. 4. Q = 21 kvar
  5. 5. ΔP = 36.29 kW
  6. 6. ΔP = 70.12 kW

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