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 19 A (rms) from a 230 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 230 VI = 19 Apf = cos φ = 0.7
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 15 A (rms) from a 240 V (rms) supply at a power factor of 0.75 lagging. Find the reactive power Q it takes.

V = 240 VI = 15 Apf = cos φ = 0.75
Q = var
3.Medium
P = 8 kWQSφ

A single-phase motor takes 8 kW at a power factor of 0.6 lagging from a 230 V supply. Find the line current I.

P = 8 kWpf = 0.6V = 230 V
I = A
4.Medium
230 VR + jXP = 782 W4 A

An inductive load takes 4 A and 782 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 4 AP = 782 W
X = Ω
5.Hard
P1​ = 14 kWQ1​S1​φ

A 50 kVA single-phase transformer supplies a load of 14 kW at a power factor of 0.65 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 = 14 kWpf1 = 0.65
ΔP = kW
6.Hard
P1​ = 48 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 48 kW at a power factor of 0.75 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 = 48 kWpf1 = 0.75
ΔP = kW

Answer key

  1. 1. Q = 3121 var
  2. 2. Q = 2381 var
  3. 3. I = 57.97 A
  4. 4. X = 30.29 Ω
  5. 5. ΔP = 33.25 kW
  6. 6. ΔP = 147.5 kW

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