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 16 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 = 16 Apf = cos φ = 0.65
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 12 A (rms) from a 400 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 400 VI = 12 Apf = cos φ = 0.8
P = W
3.Medium
230 V117 kW, 0.828 kW, 1I = ?

Two loads are connected in parallel to a 230 V single-phase supply: a 17 kW load at a power factor of 0.8 lagging and an 8 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 230 VP1 = 17 kW, pf1 = 0.8 laggingP2 = 8 kW, pf2 = 1
I = A
4.Medium
230 V19 kW, 0.65213 kW, 1I

Two loads are connected in parallel to a 230 V single-phase supply: a 9 kW load at a power factor of 0.65 lagging and a 13 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 230 VP1 = 9 kW, pf1 = 0.65 laggingP2 = 13 kW, pf2 = 1
cos φ =
5.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.7 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power QC the capacitor must supply.

P = 5 kWpf1 = 0.7pf2 = 0.9V = 230 Vf = 60 Hz
QC = kvar
6.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 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 0.95. Find the capacitance C needed.

P = 35 kWpf1 = 0.75pf2 = 0.95V = 240 Vf = 60 Hz
C = µF

Answer key

  1. 1. Q = 2797 var
  2. 2. P = 3840 W
  3. 3. I = 122 A
  4. 4. cos φ = 0.9021
  5. 5. QC = 2.679 kvar
  6. 6. C = 891.7 µF

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