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 17 A (rms) from a 400 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 400 VI = 17 Apf = cos φ = 0.65
Q = var
2.Easy
240 VloadP = 1596 W9.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 9.5 A and 1596 W. Find the power factor cos φ of the load.

V = 240 VI = 9.5 AP = 1596 W
cos φ =
3.Medium
P = 24 kWQ = ?Sφ

A single-phase motor takes 24 kW at a power factor of 0.8 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 24 kWpf = 0.8V = 400 V
Q = kvar
4.Medium
230 VR + jXP = 1898 W11 A

An inductive load takes 11 A and 1898 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 = 11 AP = 1898 W
X = Ω
5.Hard
230 V50 Hzload4 kW, 0.6C100 µFI = ?

A single-phase load takes 4 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A 100 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 4 kWpf1 = 0.6V = 230 Vf = 50 HzC = 100 µF
I = A
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.6 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 5 kWpf1 = 0.6pf2 = 0.98V = 230 Vf = 60 Hz
C = µF

Answer key

  1. 1. Q = 5168 var
  2. 2. cos φ = 0.7
  3. 3. Q = 18 kvar
  4. 4. X = 13.83 Ω
  5. 5. I = 23.61 A
  6. 6. C = 283.4 µF

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