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 16 A (rms) from a 240 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 240 VI = 16 Apf = cos φ = 0.9
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 2 A (rms) from a 400 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 400 VI = 2 Apf = cos φ = 0.7
Q = var
3.Medium
P = 17 kWQ = ?Sφ

A single-phase motor takes 17 kW at a power factor of 0.65 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 17 kWpf = 0.65V = 400 V
Q = kvar
4.Medium
P = 35 kWQ = ?Sφ

A single-phase motor takes 35 kW at a power factor of 0.85 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 35 kWpf = 0.85V = 240 V
Q = kvar
5.Hard
120 V50 HzRs​ = 20 ΩXs​ = j15 ΩZL​ = ?

A 120 V (rms), 50 Hz source has an internal impedance Zs = 20 + j15 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 120 V (rms)f = 50 HzZs = 20 + j15 Ω
Pmax = W
6.Hard
400 V50 Hzload30 kW, 0.7C100 µFI = ?

A single-phase load takes 30 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A 100 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 30 kWpf1 = 0.7V = 400 Vf = 50 HzC = 100 µF
I = A

Answer key

  1. 1. P = 3456 W
  2. 2. Q = 571.3 var
  3. 3. Q = 19.88 kvar
  4. 4. Q = 21.69 kvar
  5. 5. Pmax = 180 W
  6. 6. I = 98.56 A

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