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
230 VloadP = 690 W4 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 4 A and 690 W. Find the reactive power Q taken by the load.

V = 230 VI = 4 AP = 690 W
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 7 A (rms) from a 120 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 120 VI = 7 Apf = cos φ = 0.85
P = W
3.Medium
P = 1 kWQSφ

A single-phase motor takes 1 kW at a power factor of 0.8 lagging from a 230 V supply. Find the line current I.

P = 1 kWpf = 0.8V = 230 V
I = A
4.Medium
P = 26 kWQ = ?Sφ

A single-phase motor takes 26 kW at a power factor of 0.75 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 26 kWpf = 0.75V = 240 V
Q = kvar
5.Hard
12 V50 HzRs​ = 4 ΩXs​ = j10 ΩZL​ = ?

A 12 V (rms), 50 Hz source has an internal impedance Zs = 4 + j10 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 12 V (rms)f = 50 HzZs = 4 + j10 Ω
C = µF
6.Hard
240 V60 Hzload5 kW, 0.6C33 µFI

A single-phase load takes 5 kW at a power factor of 0.6 lagging from a 240 V, 60 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 = 5 kWpf1 = 0.6V = 240 Vf = 60 HzC = 33 µF
cos φ =

Answer key

  1. 1. Q = 608.5 var
  2. 2. P = 714 W
  3. 3. I = 5.435 A
  4. 4. Q = 22.93 kvar
  5. 5. C = 318.3 µF
  6. 6. cos φ = 0.6433

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