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
120 VloadP = 1008 W14 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 14 A and 1008 W. Find the reactive power Q taken by the load.

V = 120 VI = 14 AP = 1008 W
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 16 A (rms) from a 230 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 230 VI = 16 Apf = cos φ = 0.75
P = W
3.Medium
P = 28 kWQ = ?Sφ

A single-phase motor takes 28 kW at a power factor of 0.6 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 28 kWpf = 0.6V = 240 V
Q = kvar
4.Medium
P = 32 kWQ = ?Sφ

A single-phase motor takes 32 kW at a power factor of 0.8 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 32 kWpf = 0.8V = 230 V
Q = kvar
5.Hard
400 V50 Hzload16 kW, 0.7C33 µFI

A single-phase load takes 16 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A 33 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 16 kWpf1 = 0.7V = 400 Vf = 50 HzC = 33 µF
cos φ =
6.Hard
10 V50 HzRs​ = 10 ΩXs​ = j5 ΩZL​ = ?

A 10 V (rms), 50 Hz source has an internal impedance Zs = 10 + j5 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 = 50 HzZs = 10 + j5 Ω
Pmax = W

Answer key

  1. 1. Q = 1344 var
  2. 2. P = 2760 W
  3. 3. Q = 37.33 kvar
  4. 4. Q = 24 kvar
  5. 5. cos φ = 0.7372
  6. 6. Pmax = 2.5 W

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