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 = 50 kWQ = 32 kvarS = ?φ

A load takes 50 kW of real power and 32 kvar of reactive power (lagging). Find the apparent power S.

P = 50 kWQ = 32 kvar
S = kVA
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 9 A (rms) from a 400 V (rms) supply at a power factor of 0.7 lagging. Find the real power P it takes.

V = 400 VI = 9 Apf = cos φ = 0.7
P = W
3.Medium
P = 23 kWQ = ?Sφ

A single-phase motor takes 23 kW at a power factor of 0.65 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 23 kWpf = 0.65V = 400 V
Q = kvar
4.Medium
P = 4 kWQ = ?Sφ

A single-phase motor takes 4 kW at a power factor of 0.6 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 4 kWpf = 0.6V = 240 V
Q = kvar
5.Hard
P1​ = 6 kWQ1​S1​φ

A 15 kVA single-phase transformer supplies a load of 6 kW at a power factor of 0.6 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 15 kVAP1 = 6 kWpf1 = 0.6
ΔP = kW
6.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the reactive power QC the capacitor must supply.

P = 40 kWpf1 = 0.6pf2 = 0.98V = 230 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. S = 59.36 kVA
  2. 2. P = 2520 W
  3. 3. Q = 26.89 kvar
  4. 4. Q = 5.333 kvar
  5. 5. ΔP = 6.689 kW
  6. 6. QC = 45.21 kvar

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