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
230 VloadP = 3226 W16.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 16.5 A and 3226 W. Find the power factor cos φ of the load.

V = 230 VI = 16.5 AP = 3226 W
cos φ =
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 14 A (rms) from a 400 V (rms) supply at a power factor of 0.6 lagging. Find the real power P it takes.

V = 400 VI = 14 Apf = cos φ = 0.6
P = W
3.Medium
400 V125 kW, 0.75223 kW, 0.85I

Two loads are connected in parallel to a 400 V single-phase supply: a 25 kW load at a power factor of 0.75 lagging and a 23 kW load at a power factor of 0.85 leading. Find the overall power factor cos φ seen by the supply.

V = 400 VP1 = 25 kW, pf1 = 0.75 laggingP2 = 23 kW, pf2 = 0.85 leading
cos φ =
4.Medium
P = 27 kWQSφ

A single-phase motor takes 27 kW at a power factor of 0.65 lagging from a 400 V supply. Find the line current I.

P = 27 kWpf = 0.65V = 400 V
I = A
5.Hard
P = 10 kWQ1​S1​φ1​QC​

A single-phase load takes 10 kW at a power factor of 0.6 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current Inew.

P = 10 kWpf1 = 0.6pf2 = 0.95V = 240 Vf = 60 Hz
Inew = A
6.Hard
400 V60 Hzload21 kW, 0.65C220 µFI

A single-phase load takes 21 kW at a power factor of 0.65 lagging from a 400 V, 60 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 21 kWpf1 = 0.65V = 400 Vf = 60 HzC = 220 µF
cos φ =

Answer key

  1. 1. cos φ = 0.8501
  2. 2. P = 3360 W
  3. 3. cos φ = 0.9871
  4. 4. I = 103.8 A
  5. 5. Inew = 43.86 A
  6. 6. cos φ = 0.8809

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