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
P = 41.5 kWQ = 32 kvarSφ

A load takes 41.5 kW of real power and 32 kvar of reactive power (lagging). Find the power factor cos φ.

P = 41.5 kWQ = 32 kvar
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 13 A (rms) from a 230 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 230 VI = 13 Apf = cos φ = 0.65
Q = var
3.Medium
240 V129 kW, 0.725 kW, 0.9I

Two loads are connected in parallel to a 240 V single-phase supply: a 29 kW load at a power factor of 0.7 lagging and a 5 kW load at a power factor of 0.9 leading. Find the overall power factor cos φ seen by the supply.

V = 240 VP1 = 29 kW, pf1 = 0.7 laggingP2 = 5 kW, pf2 = 0.9 leading
cos φ =
4.Medium
P = 27 kWQSφ

A single-phase motor takes 27 kW at a power factor of 0.75 lagging from a 400 V supply. Find the line current I.

P = 27 kWpf = 0.75V = 400 V
I = A
5.Hard
100 V50 HzRs​ = 2 ΩXs​ = j20 ΩZL​ = ?

A 100 V (rms), 50 Hz source has an internal impedance Zs = 2 + j20 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 = 50 HzZs = 2 + j20 Ω
Pmax = W
6.Hard
P1​ = 109 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 109 kW at a power factor of 0.65 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 200 kVAP1 = 109 kWpf1 = 0.65
ΔP = kW

Answer key

  1. 1. cos φ = 0.7919
  2. 2. Q = 2272 var
  3. 3. cos φ = 0.7813
  4. 4. I = 90 A
  5. 5. Pmax = 1250 W
  6. 6. ΔP = 45.14 kW

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