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
PQ = ?S = V·Iφ

A single-phase load draws 14 A (rms) from a 400 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 400 VI = 14 Apf = cos φ = 0.65
Q = var
2.Easy
P = 38.5 kWQ = 9 kvarSφ

A load takes 38.5 kW of real power and 9 kvar of reactive power (lagging). Find the power factor cos φ.

P = 38.5 kWQ = 9 kvar
cos φ =
3.Medium
240 VR + jXP = 1080 W9 A

An inductive load takes 9 A and 1080 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 = 9 AP = 1080 W
X = Ω
4.Medium
P = 22 kWQSφ

A single-phase motor takes 22 kW at a power factor of 0.7 lagging from a 400 V supply. Find the line current I.

P = 22 kWpf = 0.7V = 400 V
I = A
5.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.65 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the new line current Inew.

P = 15 kWpf1 = 0.65pf2 = 0.98V = 240 Vf = 60 Hz
Inew = A
6.Hard
50 V50 HzRs​ = 5 ΩXs​ = j30 ΩZL​ = ?

A 50 V (rms), 50 Hz source has an internal impedance Zs = 5 + j30 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 50 V (rms)f = 50 HzZs = 5 + j30 Ω
Pmax = W

Answer key

  1. 1. Q = 4256 var
  2. 2. cos φ = 0.9737
  3. 3. X = 23.09 Ω
  4. 4. I = 78.57 A
  5. 5. Inew = 63.78 A
  6. 6. Pmax = 125 W

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