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 17 A (rms) from a 120 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 120 VI = 17 Apf = cos φ = 0.85
Q = var
2.Easy
P = 22 kWQ = 6.5 kvarS = ?φ

A load takes 22 kW of real power and 6.5 kvar of reactive power (lagging). Find the apparent power S.

P = 22 kWQ = 6.5 kvar
S = kVA
3.Medium
120 VZ5 + j12 ΩI

A load with impedance Z = 5 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 5 + j12 Ω
Q = var
4.Medium
P = 5 kWQ = ?Sφ

A single-phase motor takes 5 kW at a power factor of 0.7 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 5 kWpf = 0.7V = 400 V
Q = kvar
5.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 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 0.98. Find the reactive power QC the capacitor must supply.

P = 5 kWpf1 = 0.7pf2 = 0.98V = 230 Vf = 50 Hz
QC = kvar
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 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 0.92. Find the reactive power QC the capacitor must supply.

P = 20 kWpf1 = 0.6pf2 = 0.92V = 230 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. Q = 1075 var
  2. 2. S = 22.94 kVA
  3. 3. Q = 1022 var
  4. 4. Q = 5.101 kvar
  5. 5. QC = 4.086 kvar
  6. 6. QC = 18.15 kvar

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