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 7 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 120 VI = 7 Apf = cos φ = 0.65
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 3 A (rms) from a 120 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 120 VI = 3 Apf = cos φ = 0.8
Q = var
3.Medium
P = 3 kWQSφ

A single-phase motor takes 3 kW at a power factor of 0.8 lagging from a 230 V supply. Find the line current I.

P = 3 kWpf = 0.8V = 230 V
I = A
4.Medium
P = 38 kWQSφ

A single-phase motor takes 38 kW at a power factor of 0.65 lagging from a 240 V supply. Find the line current I.

P = 38 kWpf = 0.65V = 240 V
I = A
5.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 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 new line current Inew.

P = 15 kWpf1 = 0.65pf2 = 0.9V = 400 Vf = 50 Hz
Inew = A
6.Hard
P1​ = 25 kWQ1​S1​φ

A 50 kVA single-phase transformer supplies a load of 25 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 = 50 kVAP1 = 25 kWpf1 = 0.8
ΔP = kW

Answer key

  1. 1. P = 546 W
  2. 2. Q = 216 var
  3. 3. I = 16.3 A
  4. 4. I = 243.6 A
  5. 5. Inew = 41.67 A
  6. 6. ΔP = 21.35 kW

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