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 5 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 = 5 Apf = cos φ = 0.6
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 14 A (rms) from a 400 V (rms) supply at a power factor of 0.6 lagging. Find the real power P it takes.

V = 400 VI = 14 Apf = cos φ = 0.6
P = W
3.Medium
240 VZ24 + j7 ΩI

A load with impedance Z = 24 + j7 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 24 + j7 Ω
P = W
4.Medium
120 VR + jXP = 624 W6.5 A

An inductive load takes 6.5 A and 624 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 6.5 AP = 624 W
X = Ω
5.Hard
400 V50 Hzload10 kW, 0.8C22 µFI

A single-phase load takes 10 kW at a power factor of 0.8 lagging from a 400 V, 50 Hz supply. A 22 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 10 kWpf1 = 0.8V = 400 Vf = 50 HzC = 22 µF
cos φ =
6.Hard
P1​ = 29 kWQ1​S1​φ

A 75 kVA single-phase transformer supplies a load of 29 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 = 75 kVAP1 = 29 kWpf1 = 0.8
ΔP = kW

Answer key

  1. 1. Q = 1600 var
  2. 2. P = 3360 W
  3. 3. P = 2212 W
  4. 4. X = 11.08 Ω
  5. 5. cos φ = 0.8425
  6. 6. ΔP = 42.78 kW

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