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
230 Vload24.5 kW, 17.5 kvarI = ?

A single-phase load connected to a 230 V supply takes 24.5 kW and 17.5 kvar. Find the current I drawn from the supply.

V = 230 VP = 24.5 kWQ = 17.5 kvar
I = A
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 11 A (rms) from a 400 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 400 VI = 11 Apf = cos φ = 0.75
P = W
3.Medium
240 VZ4 + j3 ΩI

A load with impedance Z = 4 + j3 Ω is connected to a 240 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 240 VZ = 4 + j3 Ω
Q = var
4.Medium
P = 37 kWQSφ

A single-phase motor takes 37 kW at a power factor of 0.7 lagging from a 240 V supply. Find the line current I.

P = 37 kWpf = 0.7V = 240 V
I = A
5.Hard
230 V60 Hzload25 kW, 0.6C220 µFI

A single-phase load takes 25 kW at a power factor of 0.6 lagging from a 230 V, 60 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 = 25 kWpf1 = 0.6V = 230 Vf = 60 HzC = 220 µF
cos φ =
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.75 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 30 kWpf1 = 0.75pf2 = 0.92V = 240 Vf = 60 Hz
C = µF

Answer key

  1. 1. I = 130.9 A
  2. 2. P = 3300 W
  3. 3. Q = 6912 var
  4. 4. I = 220.2 A
  5. 5. cos φ = 0.6536
  6. 6. C = 629.9 µF

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