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 11 A (rms) from a 230 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 230 VI = 11 Apf = cos φ = 0.8
Q = var
2.Easy
230 VloadP = 2691 W13 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 13 A and 2691 W. Find the power factor cos φ of the load.

V = 230 VI = 13 AP = 2691 W
cos φ =
3.Medium
400 V129 kW, 0.628 kW, 1I

Two loads are connected in parallel to a 400 V single-phase supply: a 29 kW load at a power factor of 0.6 lagging and an 8 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP1 = 29 kW, pf1 = 0.6 laggingP2 = 8 kW, pf2 = 1
cos φ =
4.Medium
240 VR + jXP = 1632 W8 A

An inductive load takes 8 A and 1632 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 8 AP = 1632 W
R = Ω
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, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the reactive power QC the capacitor must supply.

P = 50 kWpf1 = 0.65pf2 = 0.92V = 240 Vf = 60 Hz
QC = kvar
6.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the reactive power QC the capacitor must supply.

P = 25 kWpf1 = 0.7pf2 = 0.95V = 230 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. Q = 1518 var
  2. 2. cos φ = 0.9
  3. 3. cos φ = 0.6914
  4. 4. R = 25.5 Ω
  5. 5. QC = 37.16 kvar
  6. 6. QC = 17.29 kvar

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