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 9 A (rms) from a 230 V (rms) supply at a power factor of 0.75 lagging. Find the reactive power Q it takes.

V = 230 VI = 9 Apf = cos φ = 0.75
Q = var
2.Easy
P = 45 kWQ = 29 kvarS = ?φ

A load takes 45 kW of real power and 29 kvar of reactive power (lagging). Find the apparent power S.

P = 45 kWQ = 29 kvar
S = kVA
3.Medium
P = 39 kWQSφ

A single-phase motor takes 39 kW at a power factor of 0.7 lagging from a 240 V supply. Find the line current I.

P = 39 kWpf = 0.7V = 240 V
I = A
4.Medium
P = 36 kWQSφ

A single-phase motor takes 36 kW at a power factor of 0.7 lagging from a 400 V supply. Find the line current I.

P = 36 kWpf = 0.7V = 400 V
I = A
5.Hard
50 V60 HzRs​ = 50 ΩXs​ = j3 ΩZL​ = ?

A 50 V (rms), 60 Hz source has an internal impedance Zs = 50 + j3 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 = 60 HzZs = 50 + j3 Ω
Pmax = W
6.Hard
120 V1000 HzRs​ = 8 ΩXs​ = j6 ΩZL​ = ?

A 120 V (rms), 1000 Hz source has an internal impedance Zs = 8 + j6 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 120 V (rms)f = 1000 HzZs = 8 + j6 Ω
C = µF

Answer key

  1. 1. Q = 1369 var
  2. 2. S = 53.54 kVA
  3. 3. I = 232.1 A
  4. 4. I = 128.6 A
  5. 5. Pmax = 12.5 W
  6. 6. C = 26.53 µF

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