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 = 34 kWQ = 34.5 kvarSφ

A load takes 34 kW of real power and 34.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 34 kWQ = 34.5 kvar
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 18 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 120 VI = 18 Apf = cos φ = 0.65
Q = var
3.Medium
240 VR + jXP = 2856 W14 A

An inductive load takes 14 A and 2856 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 240 VI = 14 AP = 2856 W
X = Ω
4.Medium
120 VR + jXP = 585 W6.5 A

An inductive load takes 6.5 A and 585 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 = 585 W
X = Ω
5.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.8 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 40 kWpf1 = 0.8pf2 = 0.98V = 230 Vf = 60 Hz
C = µF
6.Hard
P1​ = 64 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 64 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 = 150 kVAP1 = 64 kWpf1 = 0.65
ΔP = kW

Answer key

  1. 1. cos φ = 0.7019
  2. 2. Q = 1641 var
  3. 3. X = 9.031 Ω
  4. 4. X = 12.21 Ω
  5. 5. C = 1097 µF
  6. 6. ΔP = 66.01 kW

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