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 = 39.5 kWQ = 41.5 kvarS = ?φ

A load takes 39.5 kW of real power and 41.5 kvar of reactive power (lagging). Find the apparent power S.

P = 39.5 kWQ = 41.5 kvar
S = kVA
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 10 A (rms) from a 240 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 240 VI = 10 Apf = cos φ = 0.7
Q = var
3.Medium
P = 13 kWQSφ

A single-phase motor takes 13 kW at a power factor of 0.9 lagging from a 230 V supply. Find the line current I.

P = 13 kWpf = 0.9V = 230 V
I = A
4.Medium
P = 35 kWQ = ?Sφ

A single-phase motor takes 35 kW at a power factor of 0.9 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 35 kWpf = 0.9V = 400 V
Q = kvar
5.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 kW at a power factor of 0.7 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 35 kWpf1 = 0.7pf2 = 0.92V = 240 Vf = 50 Hz
Inew = A
6.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 35 kWpf1 = 0.65pf2 = 0.92V = 400 Vf = 50 Hz
C = µF

Answer key

  1. 1. S = 57.29 kVA
  2. 2. Q = 1714 var
  3. 3. I = 62.8 A
  4. 4. Q = 16.95 kvar
  5. 5. Inew = 158.5 A
  6. 6. C = 517.4 µF

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