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 14 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 240 VI = 14 Apf = cos φ = 0.85
P = W
2.Easy
230 Vload6.5 kW, 7.5 kvarI = ?

A single-phase load connected to a 230 V supply takes 6.5 kW and 7.5 kvar. Find the current I drawn from the supply.

V = 230 VP = 6.5 kWQ = 7.5 kvar
I = A
3.Medium
P = 35 kWQ = ?Sφ

A single-phase motor takes 35 kW at a power factor of 0.7 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 35 kWpf = 0.7V = 400 V
Q = kvar
4.Medium
120 VZ12 + j5 ΩI

A load with impedance Z = 12 + j5 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 12 + j5 Ω
P = W
5.Hard
P1​ = 55 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 55 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 = 200 kVAP1 = 55 kWpf1 = 0.85
ΔP = kW
6.Hard
P1​ = 81 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 81 kW at a power factor of 0.6 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 = 81 kWpf1 = 0.6
ΔP = kW

Answer key

  1. 1. P = 2856 W
  2. 2. I = 43.15 A
  3. 3. Q = 35.71 kvar
  4. 4. P = 1022 W
  5. 5. ΔP = 142.1 kW
  6. 6. ΔP = 87.33 kW

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