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 = 37.5 kWQ = 12 kvarSφ

A load takes 37.5 kW of real power and 12 kvar of reactive power (lagging). Find the power factor cos φ.

P = 37.5 kWQ = 12 kvar
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 3 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 = 3 Apf = cos φ = 0.95
Q = var
3.Medium
P = 18 kWQ = ?Sφ

A single-phase motor takes 18 kW at a power factor of 0.8 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 18 kWpf = 0.8V = 230 V
Q = kvar
4.Medium
P = 39 kWQ = ?Sφ

A single-phase motor takes 39 kW at a power factor of 0.85 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 39 kWpf = 0.85V = 240 V
Q = kvar
5.Hard
P1​ = 55 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 55 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 = 150 kVAP1 = 55 kWpf1 = 0.8
ΔP = kW
6.Hard
100 V50 HzRs​ = 2 ΩXs​ = j10 ΩZL​ = ?

A 100 V (rms), 50 Hz source has an internal impedance Zs = 2 + j10 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 100 V (rms)f = 50 HzZs = 2 + j10 Ω
Pmax = W

Answer key

  1. 1. cos φ = 0.9524
  2. 2. Q = 224.8 var
  3. 3. Q = 13.5 kvar
  4. 4. Q = 24.17 kvar
  5. 5. ΔP = 89.22 kW
  6. 6. Pmax = 1250 W

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