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 = 39 kWQ = 31.5 kvarS = ?φ

A load takes 39 kW of real power and 31.5 kvar of reactive power (lagging). Find the apparent power S.

P = 39 kWQ = 31.5 kvar
S = kVA
2.Easy
P = 18.5 kWQ = 9.5 kvarS = ?φ

A load takes 18.5 kW of real power and 9.5 kvar of reactive power (lagging). Find the apparent power S.

P = 18.5 kWQ = 9.5 kvar
S = kVA
3.Medium
230 VZ5 + j12 ΩI

A load with impedance Z = 5 + j12 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 5 + j12 Ω
Q = var
4.Medium
240 VZ4 + j3 ΩI

A load with impedance Z = 4 + j3 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 4 + j3 Ω
P = W
5.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 kW at a power factor of 0.75 lagging from a 240 V, 60 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 = 0.75pf2 = 0.95V = 240 Vf = 60 Hz
QC = kvar
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.75 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 5 kWpf1 = 0.75pf2 = 0.9V = 230 Vf = 60 Hz
Inew = A

Answer key

  1. 1. S = 50.13 kVA
  2. 2. S = 20.8 kVA
  3. 3. Q = 3756 var
  4. 4. P = 9216 W
  5. 5. QC = 13.83 kvar
  6. 6. Inew = 24.15 A

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