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 18 A (rms) from a 120 V (rms) supply at a power factor of 0.75 lagging. Find the reactive power Q it takes.

V = 120 VI = 18 Apf = cos φ = 0.75
Q = var
2.Easy
240 VloadP = 2700 W15 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 15 A and 2700 W. Find the power factor cos φ of the load.

V = 240 VI = 15 AP = 2700 W
cos φ =
3.Medium
120 VR + jXP = 1275 W12.5 A

An inductive load takes 12.5 A and 1275 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 = 12.5 AP = 1275 W
X = Ω
4.Medium
P = 35 kWQ = ?Sφ

A single-phase motor takes 35 kW at a power factor of 0.8 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 35 kWpf = 0.8V = 230 V
Q = kvar
5.Hard
400 V50 Hzload9 kW, 0.6C33 µFI = ?

A single-phase load takes 9 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A 33 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 9 kWpf1 = 0.6V = 400 Vf = 50 HzC = 33 µF
I = A
6.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the new line current Inew.

P = 15 kWpf1 = 0.6pf2 = 0.98V = 400 Vf = 50 Hz
Inew = A

Answer key

  1. 1. Q = 1429 var
  2. 2. cos φ = 0.75
  3. 3. X = 5.057 Ω
  4. 4. Q = 26.25 kvar
  5. 5. I = 34.27 A
  6. 6. Inew = 38.27 A

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