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
P = ?QS = V·Iφ

A single-phase load draws 18 A (rms) from a 230 V (rms) supply at a power factor of 0.7 lagging. Find the real power P it takes.

V = 230 VI = 18 Apf = cos φ = 0.7
P = W
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 16 A (rms) from a 230 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 230 VI = 16 Apf = cos φ = 0.75
P = W
3.Medium
P = 39 kWQSφ

A single-phase motor takes 39 kW at a power factor of 0.65 lagging from a 400 V supply. Find the line current I.

P = 39 kWpf = 0.65V = 400 V
I = A
4.Medium
P = 14 kWQSφ

A single-phase motor takes 14 kW at a power factor of 0.6 lagging from a 230 V supply. Find the line current I.

P = 14 kWpf = 0.6V = 230 V
I = A
5.Hard
240 V50 Hzload3 kW, 0.8C47 µFI

A single-phase load takes 3 kW at a power factor of 0.8 lagging from a 240 V, 50 Hz supply. A 47 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 3 kWpf1 = 0.8V = 240 Vf = 50 HzC = 47 µF
cos φ =
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 20 kWpf1 = 0.6pf2 = 0.92V = 400 Vf = 50 Hz
C = µF

Answer key

  1. 1. P = 2898 W
  2. 2. P = 2760 W
  3. 3. I = 150 A
  4. 4. I = 101.4 A
  5. 5. cos φ = 0.9062
  6. 6. C = 361 µF

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