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 3 A (rms) from a 230 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 230 VI = 3 Apf = cos φ = 0.9
Q = var
2.Easy
230 Vload23.5 kW, 14.5 kvarI = ?

A single-phase load connected to a 230 V supply takes 23.5 kW and 14.5 kvar. Find the current I drawn from the supply.

V = 230 VP = 23.5 kWQ = 14.5 kvar
I = A
3.Medium
230 V122 kW, 0.6526 kW, 1I = ?

Two loads are connected in parallel to a 230 V single-phase supply: a 22 kW load at a power factor of 0.65 lagging and a 6 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 230 VP1 = 22 kW, pf1 = 0.65 laggingP2 = 6 kW, pf2 = 1
I = A
4.Medium
400 V129 kW, 0.827 kW, 0.9I = ?

Two loads are connected in parallel to a 400 V single-phase supply: a 29 kW load at a power factor of 0.8 lagging and a 7 kW load at a power factor of 0.9 lagging. Find the total current I drawn from the supply.

V = 400 VP1 = 29 kW, pf1 = 0.8 laggingP2 = 7 kW, pf2 = 0.9 lagging
I = A
5.Hard
P1​ = 42 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 42 kW at a power factor of 0.85 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 = 150 kVAP1 = 42 kWpf1 = 0.85
ΔP = kW
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.65 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 20 kWpf1 = 0.65pf2 = 0.92V = 240 Vf = 60 Hz
C = µF

Answer key

  1. 1. Q = 300.8 var
  2. 2. I = 120.1 A
  3. 3. I = 165.3 A
  4. 4. I = 109.8 A
  5. 5. ΔP = 105.7 kW
  6. 6. C = 684.5 µF

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