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.

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1.Easy
PQ = ?S = V·Iφ

A single-phase load draws 3 A (rms) from a 230 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 230 VI = 3 Apf = cos φ = 0.95
Q = var
2.Easy
P = 26.5 kWQ = 16 kvarSφ

A load takes 26.5 kW of real power and 16 kvar of reactive power (lagging). Find the power factor cos φ.

P = 26.5 kWQ = 16 kvar
cos φ =
3.Medium
240 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 240 V (rms) single-phase supply. Find the apparent power S.

V = 240 VZ = 6 + j8 Ω
S = VA
4.Medium
P = 17 kWQ = ?Sφ

A single-phase motor takes 17 kW at a power factor of 0.6 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 17 kWpf = 0.6V = 230 V
Q = kvar
5.Hard
400 V50 Hzload20 kW, 0.7C47 µFI = ?

A single-phase load takes 20 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A 47 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 20 kWpf1 = 0.7V = 400 Vf = 50 HzC = 47 µF
I = A
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.65 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 50 kWpf1 = 0.65pf2 = 0.9V = 240 Vf = 50 Hz
Inew = A

Answer key

  1. 1. Q = 215.5 var
  2. 2. cos φ = 0.8561
  3. 3. S = 5760 VA
  4. 4. Q = 22.67 kvar
  5. 5. I = 67.34 A
  6. 6. Inew = 231.5 A

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