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 = 24 kWQ = 23 kvarS = ?φ

A load takes 24 kW of real power and 23 kvar of reactive power (lagging). Find the apparent power S.

P = 24 kWQ = 23 kvar
S = kVA
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 3 A (rms) from a 230 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 230 VI = 3 Apf = cos φ = 0.7
Q = var
3.Medium
400 V114 kW, 0.75224 kW, 1I

Two loads are connected in parallel to a 400 V single-phase supply: a 14 kW load at a power factor of 0.75 lagging and a 24 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP1 = 14 kW, pf1 = 0.75 laggingP2 = 24 kW, pf2 = 1
cos φ =
4.Medium
P = 3 kWQ = ?Sφ

A single-phase motor takes 3 kW at a power factor of 0.9 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 3 kWpf = 0.9V = 230 V
Q = kvar
5.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.8 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the new line current Inew.

P = 50 kWpf1 = 0.8pf2 = 0.98V = 240 Vf = 50 Hz
Inew = A
6.Hard
P = 10 kWQ1​S1​φ1​QC​

A single-phase load takes 10 kW at a power factor of 0.6 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 = 10 kWpf1 = 0.6pf2 = 0.92V = 400 Vf = 60 Hz
Inew = A

Answer key

  1. 1. S = 33.24 kVA
  2. 2. Q = 492.8 var
  3. 3. cos φ = 0.9511
  4. 4. Q = 1.453 kvar
  5. 5. Inew = 212.6 A
  6. 6. Inew = 27.17 A

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