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
120 Vload13.5 kW, 10.5 kvarI = ?

A single-phase load connected to a 120 V supply takes 13.5 kW and 10.5 kvar. Find the current I drawn from the supply.

V = 120 VP = 13.5 kWQ = 10.5 kvar
I = A
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 4 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 120 VI = 4 Apf = cos φ = 0.65
P = W
3.Medium
230 VZ20 + j15 ΩI

A load with impedance Z = 20 + j15 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 20 + j15 Ω
Q = var
4.Medium
P = 3 kWQSφ

A single-phase motor takes 3 kW at a power factor of 0.75 lagging from a 240 V supply. Find the line current I.

P = 3 kWpf = 0.75V = 240 V
I = A
5.Hard
230 V50 Hzload9 kW, 0.6C220 µFI

A single-phase load takes 9 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 9 kWpf1 = 0.6V = 230 Vf = 50 HzC = 220 µF
cos φ =
6.Hard
P1​ = 57 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 57 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 = 57 kWpf1 = 0.65
ΔP = kW

Answer key

  1. 1. I = 142.5 A
  2. 2. P = 312 W
  3. 3. Q = 1270 var
  4. 4. I = 16.67 A
  5. 5. cos φ = 0.7333
  6. 6. ΔP = 131.6 kW

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