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 2 A (rms) from a 120 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 120 VI = 2 Apf = cos φ = 0.9
P = W
2.Easy
240 VloadP = 3648 W16 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 16 A and 3648 W. Find the power factor cos φ of the load.

V = 240 VI = 16 AP = 3648 W
cos φ =
3.Medium
240 VR + jXP = 2484 W11.5 A

An inductive load takes 11.5 A and 2484 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 11.5 AP = 2484 W
R = Ω
4.Medium
P = 6 kWQ = ?Sφ

A single-phase motor takes 6 kW at a power factor of 0.8 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 6 kWpf = 0.8V = 240 V
Q = kvar
5.Hard
50 V1000 HzRs​ = 4 ΩXs​ = j15 ΩZL​ = ?

A 50 V (rms), 1000 Hz source has an internal impedance Zs = 4 + j15 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 = 1000 HzZs = 4 + j15 Ω
Pmax = W
6.Hard
P = 10 kWQ1​S1​φ1​QC​

A single-phase load takes 10 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 10 kWpf1 = 0.7pf2 = 0.9V = 230 Vf = 50 Hz
C = µF

Answer key

  1. 1. P = 216 W
  2. 2. cos φ = 0.95
  3. 3. R = 18.78 Ω
  4. 4. Q = 4.5 kvar
  5. 5. Pmax = 156.3 W
  6. 6. C = 322.5 µF

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