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 0.8 lagging. Find the reactive power Q it takes.

V = 230 VI = 10 Apf = cos φ = 0.8
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 7 A (rms) from a 230 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 230 VI = 7 Apf = cos φ = 0.9
Q = var
3.Medium
120 VZ9 + j12 ΩI

A load with impedance Z = 9 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the apparent power S.

V = 120 VZ = 9 + j12 Ω
S = VA
4.Medium
120 VR + jXP = 1632 W17 A

An inductive load takes 17 A and 1632 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 17 AP = 1632 W
X = Ω
5.Hard
230 V50 HzRs​ = 4 ΩXs​ = j3 ΩZL​ = ?

A 230 V (rms), 50 Hz source has an internal impedance Zs = 4 + j3 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 = 50 HzZs = 4 + j3 Ω
Pmax = W
6.Hard
100 V1000 HzRs​ = 4 ΩXs​ = j5 ΩZL​ = ?

A 100 V (rms), 1000 Hz source has an internal impedance Zs = 4 + j5 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 100 V (rms)f = 1000 HzZs = 4 + j5 Ω
Pmax = W

Answer key

  1. 1. Q = 1380 var
  2. 2. Q = 701.8 var
  3. 3. S = 960 VA
  4. 4. X = 4.235 Ω
  5. 5. Pmax = 3306 W
  6. 6. Pmax = 625 W

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