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 = 41 kWQ = 44.5 kvarS = ?φ

A load takes 41 kW of real power and 44.5 kvar of reactive power (lagging). Find the apparent power S.

P = 41 kWQ = 44.5 kvar
S = kVA
2.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
3.Medium
P = 24 kWQSφ

A single-phase motor takes 24 kW at a power factor of 0.85 lagging from a 400 V supply. Find the line current I.

P = 24 kWpf = 0.85V = 400 V
I = A
4.Medium
230 V115 kW, 0.65210 kW, 0.85I = ?

Two loads are connected in parallel to a 230 V single-phase supply: a 15 kW load at a power factor of 0.65 lagging and a 10 kW load at a power factor of 0.85 leading. Find the total current I drawn from the supply.

V = 230 VP1 = 15 kW, pf1 = 0.65 laggingP2 = 10 kW, pf2 = 0.85 leading
I = A
5.Hard
P1​ = 5 kWQ1​S1​φ

A 10 kVA single-phase transformer supplies a load of 5 kW at a power factor of 0.85 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 = 10 kVAP1 = 5 kWpf1 = 0.85
ΔP = kW
6.Hard
P1​ = 72 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 72 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 = 200 kVAP1 = 72 kWpf1 = 0.65
ΔP = kW

Answer key

  1. 1. S = 60.51 kVA
  2. 2. P = 2898 W
  3. 3. I = 70.59 A
  4. 4. I = 119.4 A
  5. 5. ΔP = 4.508 kW
  6. 6. ΔP = 109.4 kW

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