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
240 Vload16.5 kW, 21.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 16.5 kW and 21.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 16.5 kWQ = 21.5 kvar
I = A
2.Easy
P = 38 kWQ = 38 kvarSφ

A load takes 38 kW of real power and 38 kvar of reactive power (lagging). Find the power factor cos φ.

P = 38 kWQ = 38 kvar
cos φ =
3.Medium
230 VZ7 + j24 ΩI

A load with impedance Z = 7 + j24 Ω is connected to a 230 V (rms) single-phase supply. Find the apparent power S.

V = 230 VZ = 7 + j24 Ω
S = VA
4.Medium
P = 20 kWQ = ?Sφ

A single-phase motor takes 20 kW at a power factor of 0.85 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 20 kWpf = 0.85V = 230 V
Q = kvar
5.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 15 kWpf1 = 0.6pf2 = 0.92V = 230 Vf = 50 Hz
Inew = A
6.Hard
120 V60 HzRs​ = 5 ΩXs​ = j40 ΩZL​ = ?

A 120 V (rms), 60 Hz source has an internal impedance Zs = 5 + j40 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 = 60 HzZs = 5 + j40 Ω
C = µF

Answer key

  1. 1. I = 112.9 A
  2. 2. cos φ = 0.7071
  3. 3. S = 2116 VA
  4. 4. Q = 12.39 kvar
  5. 5. Inew = 70.89 A
  6. 6. C = 66.31 µF

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