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 5 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 120 VI = 5 Apf = cos φ = 0.65
Q = var
2.Easy
230 VloadP = 1449 W9 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 9 A and 1449 W. Find the reactive power Q taken by the load.

V = 230 VI = 9 AP = 1449 W
Q = var
3.Medium
120 VR + jXP = 672 W7 A

An inductive load takes 7 A and 672 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 = 7 AP = 672 W
X = Ω
4.Medium
P = 12 kWQSφ

A single-phase motor takes 12 kW at a power factor of 0.65 lagging from a 230 V supply. Find the line current I.

P = 12 kWpf = 0.65V = 230 V
I = A
5.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 40 kWpf1 = 0.75pf2 = 0.92V = 230 Vf = 50 Hz
Inew = A
6.Hard
240 V60 Hzload9 kW, 0.75C68 µFI

A single-phase load takes 9 kW at a power factor of 0.75 lagging from a 240 V, 60 Hz supply. A 68 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 9 kWpf1 = 0.75V = 240 Vf = 60 HzC = 68 µF
cos φ =

Answer key

  1. 1. Q = 456 var
  2. 2. Q = 1478 var
  3. 3. X = 10.29 Ω
  4. 4. I = 80.27 A
  5. 5. Inew = 189 A
  6. 6. cos φ = 0.8124

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