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 2 A (rms) from a 400 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 400 VI = 2 Apf = cos φ = 0.7
Q = var
2.Easy
P = 8.5 kWQ = 2.5 kvarS = ?φ

A load takes 8.5 kW of real power and 2.5 kvar of reactive power (lagging). Find the apparent power S.

P = 8.5 kWQ = 2.5 kvar
S = kVA
3.Medium
230 V126 kW, 0.75220 kW, 0.9I = ?

Two loads are connected in parallel to a 230 V single-phase supply: a 26 kW load at a power factor of 0.75 lagging and a 20 kW load at a power factor of 0.9 lagging. Find the total current I drawn from the supply.

V = 230 VP1 = 26 kW, pf1 = 0.75 laggingP2 = 20 kW, pf2 = 0.9 lagging
I = A
4.Medium
P = 30 kWQ = ?Sφ

A single-phase motor takes 30 kW at a power factor of 0.75 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 30 kWpf = 0.75V = 230 V
Q = kvar
5.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 15 kWpf1 = 0.65pf2 = 0.95V = 400 Vf = 50 Hz
C = µF
6.Hard
240 V60 Hzload7 kW, 0.65C68 µFI = ?

A single-phase load takes 7 kW at a power factor of 0.65 lagging from a 240 V, 60 Hz supply. A 68 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 7 kWpf1 = 0.65V = 240 Vf = 60 HzC = 68 µF
I = A

Answer key

  1. 1. Q = 571.3 var
  2. 2. S = 8.86 kVA
  3. 3. I = 245.2 A
  4. 4. Q = 26.46 kvar
  5. 5. C = 250.8 µF
  6. 6. I = 40.39 A

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