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 = 3030 W15.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 15.5 A and 3030 W. Find the power factor cos φ of the load.

V = 230 VI = 15.5 AP = 3030 W
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 17 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 = 17 Apf = cos φ = 0.65
Q = var
3.Medium
240 VZ3 + j4 ΩI

A load with impedance Z = 3 + j4 Ω is connected to a 240 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 240 VZ = 3 + j4 Ω
Q = var
4.Medium
P = 19 kWQSφ

A single-phase motor takes 19 kW at a power factor of 0.8 lagging from a 240 V supply. Find the line current I.

P = 19 kWpf = 0.8V = 240 V
I = A
5.Hard
10 V50 HzRs​ = 50 ΩXs​ = j20 ΩZL​ = ?

A 10 V (rms), 50 Hz source has an internal impedance Zs = 50 + j20 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 = 50 + j20 Ω
Pmax = W
6.Hard
240 V50 Hzload21 kW, 0.75C470 µFI

A single-phase load takes 21 kW at a power factor of 0.75 lagging from a 240 V, 50 Hz supply. A 470 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 21 kWpf1 = 0.75V = 240 Vf = 50 HzC = 470 µF
cos φ =

Answer key

  1. 1. cos φ = 0.8499
  2. 2. Q = 3101 var
  3. 3. Q = 9216 var
  4. 4. I = 98.96 A
  5. 5. Pmax = 0.5 W
  6. 6. cos φ = 0.9026

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