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
120 VloadP = 819 W10.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 10.5 A and 819 W. Find the power factor cos φ of the load.

V = 120 VI = 10.5 AP = 819 W
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 8 A (rms) from a 400 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 400 VI = 8 Apf = cos φ = 0.8
Q = var
3.Medium
P = 1 kWQ = ?Sφ

A single-phase motor takes 1 kW at a power factor of 0.75 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 1 kWpf = 0.75V = 400 V
Q = kvar
4.Medium
P = 17 kWQ = ?Sφ

A single-phase motor takes 17 kW at a power factor of 0.6 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 17 kWpf = 0.6V = 230 V
Q = kvar
5.Hard
240 V50 Hzload8 kW, 0.65C100 µFI

A single-phase load takes 8 kW at a power factor of 0.65 lagging from a 240 V, 50 Hz supply. A 100 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 8 kWpf1 = 0.65V = 240 Vf = 50 HzC = 100 µF
cos φ =
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 50 kWpf1 = 0.65pf2 = 0.9V = 400 Vf = 50 Hz
C = µF

Answer key

  1. 1. cos φ = 0.65
  2. 2. Q = 1920 var
  3. 3. Q = 0.8819 kvar
  4. 4. Q = 22.67 kvar
  5. 5. cos φ = 0.7276
  6. 6. C = 681.2 µF

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