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 = 39 kWQ = 11 kvarS = ?φ

A load takes 39 kW of real power and 11 kvar of reactive power (lagging). Find the apparent power S.

P = 39 kWQ = 11 kvar
S = kVA
2.Easy
120 VloadP = 1755 W19.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 19.5 A and 1755 W. Find the reactive power Q taken by the load.

V = 120 VI = 19.5 AP = 1755 W
Q = var
3.Medium
P = 24 kWQSφ

A single-phase motor takes 24 kW at a power factor of 0.9 lagging from a 230 V supply. Find the line current I.

P = 24 kWpf = 0.9V = 230 V
I = A
4.Medium
230 VR + jXP = 2174 W13.5 A

An inductive load takes 13.5 A and 2174 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 13.5 AP = 2174 W
R = Ω
5.Hard
P1​ = 92 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 92 kW at a power factor of 0.85 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 = 92 kWpf1 = 0.85
ΔP = kW
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.65 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 20 kWpf1 = 0.65pf2 = 0.98V = 230 Vf = 50 Hz
C = µF

Answer key

  1. 1. S = 40.52 kVA
  2. 2. Q = 1548 var
  3. 3. I = 115.9 A
  4. 4. R = 11.93 Ω
  5. 5. ΔP = 46.74 kW
  6. 6. C = 1163 µF

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