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 = 24.5 kWQ = 16 kvarSφ

A load takes 24.5 kW of real power and 16 kvar of reactive power (lagging). Find the power factor cos φ.

P = 24.5 kWQ = 16 kvar
cos φ =
2.Easy
120 Vload20 kW, 9 kvarI = ?

A single-phase load connected to a 120 V supply takes 20 kW and 9 kvar. Find the current I drawn from the supply.

V = 120 VP = 20 kWQ = 9 kvar
I = A
3.Medium
P = 28 kWQ = ?Sφ

A single-phase motor takes 28 kW at a power factor of 0.75 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 28 kWpf = 0.75V = 230 V
Q = kvar
4.Medium
230 V12 kW, 0.85227 kW, 0.9I

Two loads are connected in parallel to a 230 V single-phase supply: a 2 kW load at a power factor of 0.85 lagging and a 27 kW load at a power factor of 0.9 lagging. Find the overall power factor cos φ seen by the supply.

V = 230 VP1 = 2 kW, pf1 = 0.85 laggingP2 = 27 kW, pf2 = 0.9 lagging
cos φ =
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 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 15 kWpf1 = 0.65pf2 = 0.9V = 230 Vf = 60 Hz
C = µF
6.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 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 capacitance C needed.

P = 40 kWpf1 = 0.7pf2 = 0.9V = 230 Vf = 60 Hz
C = µF

Answer key

  1. 1. cos φ = 0.8373
  2. 2. I = 182.8 A
  3. 3. Q = 24.69 kvar
  4. 4. cos φ = 0.8967
  5. 5. C = 515.1 µF
  6. 6. C = 1075 µF

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