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 7 A (rms) from a 120 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 120 VI = 7 Apf = cos φ = 0.95
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 9 A (rms) from a 230 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 230 VI = 9 Apf = cos φ = 0.85
Q = var
3.Medium
230 VR + jXP = 460 W2.5 A

An inductive load takes 2.5 A and 460 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 = 2.5 AP = 460 W
R = Ω
4.Medium
120 VR + jXP = 648 W9 A

An inductive load takes 9 A and 648 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 9 AP = 648 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 240 V, 50 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 = 240 Vf = 50 Hz
Inew = A
6.Hard
230 V60 Hzload25 kW, 0.65C220 µFI = ?

A single-phase load takes 25 kW at a power factor of 0.65 lagging from a 230 V, 60 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 25 kWpf1 = 0.65V = 230 Vf = 60 HzC = 220 µF
I = A

Answer key

  1. 1. Q = 262.3 var
  2. 2. Q = 1090 var
  3. 3. R = 73.6 Ω
  4. 4. X = 10.67 Ω
  5. 5. Inew = 115.7 A
  6. 6. I = 153.2 A

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