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 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
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 3 A (rms) from a 240 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 240 VI = 3 Apf = cos φ = 0.8
P = W
3.Medium
P = 17 kWQSφ

A single-phase motor takes 17 kW at a power factor of 0.9 lagging from a 240 V supply. Find the line current I.

P = 17 kWpf = 0.9V = 240 V
I = A
4.Medium
P = 4 kWQSφ

A single-phase motor takes 4 kW at a power factor of 0.65 lagging from a 400 V supply. Find the line current I.

P = 4 kWpf = 0.65V = 400 V
I = A
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.75 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 20 kWpf1 = 0.75pf2 = 0.98V = 400 Vf = 50 Hz
C = µF
6.Hard
24 V50 HzRs​ = 8 ΩXs​ = j30 ΩZL​ = ?

A 24 V (rms), 50 Hz source has an internal impedance Zs = 8 + j30 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 24 V (rms)f = 50 HzZs = 8 + j30 Ω
Pmax = W

Answer key

  1. 1. Q = 576 var
  2. 2. P = 576 W
  3. 3. I = 78.7 A
  4. 4. I = 15.38 A
  5. 5. C = 270.1 µF
  6. 6. Pmax = 18 W

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