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
P = ?QS = V·Iφ

A single-phase load draws 17 A (rms) from a 400 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 400 VI = 17 Apf = cos φ = 0.75
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 13 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 400 VI = 13 Apf = cos φ = 0.9
Q = var
3.Medium
P = 36 kWQ = ?Sφ

A single-phase motor takes 36 kW at a power factor of 0.7 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 36 kWpf = 0.7V = 230 V
Q = kvar
4.Medium
120 VZ16 + j12 ΩI

A load with impedance Z = 16 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the apparent power S.

V = 120 VZ = 16 + j12 Ω
S = VA
5.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the new line current Inew.

P = 40 kWpf1 = 0.8pf2 = 0.98V = 400 Vf = 60 Hz
Inew = A
6.Hard
P = 45 kWQ1​S1​φ1​QC​

A single-phase load takes 45 kW at a power factor of 0.7 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 45 kWpf1 = 0.7pf2 = 0.9V = 240 Vf = 60 Hz
Inew = A

Answer key

  1. 1. P = 5100 W
  2. 2. Q = 2267 var
  3. 3. Q = 36.73 kvar
  4. 4. S = 720 VA
  5. 5. Inew = 102 A
  6. 6. Inew = 208.3 A

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