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 11 A (rms) from a 120 V (rms) supply at a power factor of 0.95 lagging. Find the real power P it takes.

V = 120 VI = 11 Apf = cos φ = 0.95
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 12 A (rms) from a 240 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 240 VI = 12 Apf = cos φ = 0.8
Q = var
3.Medium
240 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 6 + j8 Ω
P = W
4.Medium
P = 29 kWQ = ?Sφ

A single-phase motor takes 29 kW at a power factor of 0.7 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 29 kWpf = 0.7V = 240 V
Q = kvar
5.Hard
P1​ = 49 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 49 kW at a power factor of 0.6 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 = 49 kWpf1 = 0.6
ΔP = kW
6.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 40 kWpf1 = 0.75pf2 = 0.9V = 230 Vf = 50 Hz
C = µF

Answer key

  1. 1. P = 1254 W
  2. 2. Q = 1728 var
  3. 3. P = 3456 W
  4. 4. Q = 29.59 kvar
  5. 5. ΔP = 86.02 kW
  6. 6. C = 957 µF

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