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 10 A (rms) from a 230 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 230 VI = 10 Apf = cos φ = 0.85
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 17 A (rms) from a 120 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 120 VI = 17 Apf = cos φ = 0.75
P = W
3.Medium
P = 38 kWQ = ?Sφ

A single-phase motor takes 38 kW at a power factor of 0.7 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 38 kWpf = 0.7V = 240 V
Q = kvar
4.Medium
P = 10 kWQ = ?Sφ

A single-phase motor takes 10 kW at a power factor of 0.75 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 10 kWpf = 0.75V = 400 V
Q = kvar
5.Hard
400 V60 Hzload17 kW, 0.65C68 µFI = ?

A single-phase load takes 17 kW at a power factor of 0.65 lagging from a 400 V, 60 Hz supply. A 68 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 17 kWpf1 = 0.65V = 400 Vf = 60 HzC = 68 µF
I = A
6.Hard
230 V60 HzRs​ = 10 ΩXs​ = j40 ΩZL​ = ?

A 230 V (rms), 60 Hz source has an internal impedance Zs = 10 + j40 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 230 V (rms)f = 60 HzZs = 10 + j40 Ω
Pmax = W

Answer key

  1. 1. Q = 1212 var
  2. 2. P = 1530 W
  3. 3. Q = 38.77 kvar
  4. 4. Q = 8.819 kvar
  5. 5. I = 57.98 A
  6. 6. Pmax = 1323 W

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