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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
P = ?QS = V·Iφ

A single-phase load draws 8 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 400 VI = 8 Apf = cos φ = 0.9
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 3 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 3 Apf = cos φ = 0.6
Q = var
3.Medium
230 VR + jXP = 2174 W13.5 A

An inductive load takes 13.5 A and 2174 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 13.5 AP = 2174 W
R = Ω
4.Medium
230 VZ3 + j4 ΩI

A load with impedance Z = 3 + j4 Ω is connected to a 230 V (rms) single-phase supply. Find the apparent power S.

V = 230 VZ = 3 + j4 Ω
S = VA
5.Hard
P1​ = 51 kWQ1​S1​φ

A 100 kVA single-phase transformer supplies a load of 51 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 = 51 kWpf1 = 0.75
ΔP = kW
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 30 kWpf1 = 0.65pf2 = 0.9V = 400 Vf = 50 Hz
C = µF

Answer key

  1. 1. P = 2880 W
  2. 2. Q = 576 var
  3. 3. R = 11.93 Ω
  4. 4. S = 10580 VA
  5. 5. ΔP = 38.31 kW
  6. 6. C = 408.7 µF

Full step-by-step solutions: practise this topic on examproblems.com.