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 10 A (rms) from a 240 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 240 VI = 10 Apf = cos φ = 0.9
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 7 A (rms) from a 240 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 240 VI = 7 Apf = cos φ = 0.95
Q = var
3.Medium
P = 9 kWQSφ

A single-phase motor takes 9 kW at a power factor of 0.75 lagging from a 400 V supply. Find the line current I.

P = 9 kWpf = 0.75V = 400 V
I = A
4.Medium
P = 29 kWQSφ

A single-phase motor takes 29 kW at a power factor of 0.85 lagging from a 400 V supply. Find the line current I.

P = 29 kWpf = 0.85V = 400 V
I = A
5.Hard
P1​ = 88 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 88 kW at a power factor of 0.8 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 200 kVAP1 = 88 kWpf1 = 0.8
ΔP = kW
6.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 kW at a power factor of 0.7 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 25 kWpf1 = 0.7pf2 = 0.9V = 240 Vf = 50 Hz
Inew = A

Answer key

  1. 1. Q = 1046 var
  2. 2. Q = 524.6 var
  3. 3. I = 30 A
  4. 4. I = 85.29 A
  5. 5. ΔP = 100.8 kW
  6. 6. Inew = 115.7 A

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