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 = 35.5 kWQ = 23.5 kvarSφ

A load takes 35.5 kW of real power and 23.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 35.5 kWQ = 23.5 kvar
cos φ =
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 17 A (rms) from a 120 V (rms) supply at a power factor of 0.6 lagging. Find the real power P it takes.

V = 120 VI = 17 Apf = cos φ = 0.6
P = W
3.Medium
P = 11 kWQSφ

A single-phase motor takes 11 kW at a power factor of 0.7 lagging from a 230 V supply. Find the line current I.

P = 11 kWpf = 0.7V = 230 V
I = A
4.Medium
120 VZ16 + j12 ΩI

A load with impedance Z = 16 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 16 + j12 Ω
Q = var
5.Hard
P1​ = 58 kWQ1​S1​φ

A 100 kVA single-phase transformer supplies a load of 58 kW at a power factor of 0.85 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 = 100 kVAP1 = 58 kWpf1 = 0.85
ΔP = kW
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 20 kWpf1 = 0.8pf2 = 0.92V = 400 Vf = 60 Hz
Inew = A

Answer key

  1. 1. cos φ = 0.8339
  2. 2. P = 1224 W
  3. 3. I = 68.32 A
  4. 4. Q = 432 var
  5. 5. ΔP = 35.32 kW
  6. 6. Inew = 54.35 A

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