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 13 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 = 13 Apf = cos φ = 0.75
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 3 A (rms) from a 240 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 240 VI = 3 Apf = cos φ = 0.75
P = W
3.Medium
P = 28 kWQSφ

A single-phase motor takes 28 kW at a power factor of 0.75 lagging from a 240 V supply. Find the line current I.

P = 28 kWpf = 0.75V = 240 V
I = A
4.Medium
240 V14 kW, 0.6225 kW, 0.9I

Two loads are connected in parallel to a 240 V single-phase supply: a 4 kW load at a power factor of 0.6 lagging and a 25 kW load at a power factor of 0.9 lagging. Find the overall power factor cos φ seen by the supply.

V = 240 VP1 = 4 kW, pf1 = 0.6 laggingP2 = 25 kW, pf2 = 0.9 lagging
cos φ =
5.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 50 kWpf1 = 0.7pf2 = 0.98V = 230 Vf = 50 Hz
C = µF
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.65 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 5 kWpf1 = 0.65pf2 = 0.98V = 240 Vf = 50 Hz
C = µF

Answer key

  1. 1. Q = 1032 var
  2. 2. P = 540 W
  3. 3. I = 155.6 A
  4. 4. cos φ = 0.857
  5. 5. C = 2458 µF
  6. 6. C = 266.9 µF

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