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 20 A (rms) from a 240 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 240 VI = 20 Apf = cos φ = 0.8
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 4 A (rms) from a 120 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 120 VI = 4 Apf = cos φ = 0.7
Q = var
3.Medium
P = 36 kWQ = ?Sφ

A single-phase motor takes 36 kW at a power factor of 0.8 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 36 kWpf = 0.8V = 230 V
Q = kvar
4.Medium
230 VR + jXP = 1380 W7.5 A

An inductive load takes 7.5 A and 1380 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 7.5 AP = 1380 W
X = Ω
5.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 kW at a power factor of 0.6 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 25 kWpf1 = 0.6pf2 = 0.9V = 400 Vf = 60 Hz
Inew = A
6.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 0.95. Find the new line current Inew.

P = 40 kWpf1 = 0.8pf2 = 0.95V = 400 Vf = 60 Hz
Inew = A

Answer key

  1. 1. Q = 2880 var
  2. 2. Q = 342.8 var
  3. 3. Q = 27 kvar
  4. 4. X = 18.4 Ω
  5. 5. Inew = 69.44 A
  6. 6. Inew = 105.3 A

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