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 17 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 17 Apf = cos φ = 0.6
Q = var
2.Easy
P = 46.5 kWQ = 39 kvarS = ?φ

A load takes 46.5 kW of real power and 39 kvar of reactive power (lagging). Find the apparent power S.

P = 46.5 kWQ = 39 kvar
S = kVA
3.Medium
P = 23 kWQ = ?Sφ

A single-phase motor takes 23 kW at a power factor of 0.6 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 23 kWpf = 0.6V = 230 V
Q = kvar
4.Medium
P = 14 kWQ = ?Sφ

A single-phase motor takes 14 kW at a power factor of 0.75 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 14 kWpf = 0.75V = 400 V
Q = kvar
5.Hard
120 V50 HzRs​ = 50 ΩXs​ = j6 ΩZL​ = ?

A 120 V (rms), 50 Hz source has an internal impedance Zs = 50 + j6 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 = 50 + j6 Ω
Pmax = W
6.Hard
120 V1000 HzRs​ = 50 ΩXs​ = j20 ΩZL​ = ?

A 120 V (rms), 1000 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 = 120 V (rms)f = 1000 HzZs = 50 + j20 Ω
Pmax = W

Answer key

  1. 1. Q = 3264 var
  2. 2. S = 60.69 kVA
  3. 3. Q = 30.67 kvar
  4. 4. Q = 12.35 kvar
  5. 5. Pmax = 72 W
  6. 6. Pmax = 72 W

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