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 = ?QS = V·Iφ

A single-phase load draws 6 A (rms) from a 230 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 230 VI = 6 Apf = cos φ = 0.8
P = W
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 20 A (rms) from a 120 V (rms) supply at a power factor of 0.7 lagging. Find the real power P it takes.

V = 120 VI = 20 Apf = cos φ = 0.7
P = W
3.Medium
P = 31 kWQSφ

A single-phase motor takes 31 kW at a power factor of 0.7 lagging from a 400 V supply. Find the line current I.

P = 31 kWpf = 0.7V = 400 V
I = A
4.Medium
240 V124 kW, 0.65225 kW, 0.8I = ?

Two loads are connected in parallel to a 240 V single-phase supply: a 24 kW load at a power factor of 0.65 lagging and a 25 kW load at a power factor of 0.8 leading. Find the total current I drawn from the supply.

V = 240 VP1 = 24 kW, pf1 = 0.65 laggingP2 = 25 kW, pf2 = 0.8 leading
I = A
5.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.65 lagging from a 240 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 = 50 kWpf1 = 0.65pf2 = 0.98V = 240 Vf = 50 Hz
QC = kvar
6.Hard
P = 10 kWQ1​S1​φ1​QC​

A single-phase load takes 10 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the reactive power QC the capacitor must supply.

P = 10 kWpf1 = 0.8pf2 = 0.98V = 400 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. P = 1104 W
  2. 2. P = 1680 W
  3. 3. I = 110.7 A
  4. 4. I = 207.8 A
  5. 5. QC = 48.3 kvar
  6. 6. QC = 5.469 kvar

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