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 18 A (rms) from a 240 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 240 VI = 18 Apf = cos φ = 0.65
Q = var
2.Easy
P = 42 kWQ = 16.5 kvarS = ?φ

A load takes 42 kW of real power and 16.5 kvar of reactive power (lagging). Find the apparent power S.

P = 42 kWQ = 16.5 kvar
S = kVA
3.Medium
P = 30 kWQSφ

A single-phase motor takes 30 kW at a power factor of 0.9 lagging from a 400 V supply. Find the line current I.

P = 30 kWpf = 0.9V = 400 V
I = A
4.Medium
P = 5 kWQ = ?Sφ

A single-phase motor takes 5 kW at a power factor of 0.85 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 5 kWpf = 0.85V = 400 V
Q = kvar
5.Hard
230 V60 Hzload26 kW, 0.65C330 µFI

A single-phase load takes 26 kW at a power factor of 0.65 lagging from a 230 V, 60 Hz supply. A 330 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 26 kWpf1 = 0.65V = 230 Vf = 60 HzC = 330 µF
cos φ =
6.Hard
10 V60 HzRs​ = 4 ΩXs​ = j30 ΩZL​ = ?

A 10 V (rms), 60 Hz source has an internal impedance Zs = 4 + j30 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 10 V (rms)f = 60 HzZs = 4 + j30 Ω
Pmax = W

Answer key

  1. 1. Q = 3283 var
  2. 2. S = 45.12 kVA
  3. 3. I = 83.33 A
  4. 4. Q = 3.099 kvar
  5. 5. cos φ = 0.7374
  6. 6. Pmax = 6.25 W

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