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 = 35.5 kWQ = 13 kvarS = ?φ

A load takes 35.5 kW of real power and 13 kvar of reactive power (lagging). Find the apparent power S.

P = 35.5 kWQ = 13 kvar
S = kVA
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 13 A (rms) from a 230 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 230 VI = 13 Apf = cos φ = 0.85
P = W
3.Medium
P = 21 kWQ = ?Sφ

A single-phase motor takes 21 kW at a power factor of 0.6 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 21 kWpf = 0.6V = 230 V
Q = kvar
4.Medium
400 V14 kW, 0.65228 kW, 1I

Two loads are connected in parallel to a 400 V single-phase supply: a 4 kW load at a power factor of 0.65 lagging and a 28 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP1 = 4 kW, pf1 = 0.65 laggingP2 = 28 kW, pf2 = 1
cos φ =
5.Hard
P1​ = 52 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 52 kW at a power factor of 0.7 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 = 200 kVAP1 = 52 kWpf1 = 0.7
ΔP = kW
6.Hard
P1​ = 84 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 84 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 = 200 kVAP1 = 84 kWpf1 = 0.8
ΔP = kW

Answer key

  1. 1. S = 37.81 kVA
  2. 2. P = 2542 W
  3. 3. Q = 28 kvar
  4. 4. cos φ = 0.9895
  5. 5. ΔP = 140.8 kW
  6. 6. ΔP = 105.8 kW

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