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 = 22.5 kWQ = 12.5 kvarSφ

A load takes 22.5 kW of real power and 12.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 22.5 kWQ = 12.5 kvar
cos φ =
2.Easy
230 VloadP = 431 W2.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 2.5 A and 431 W. Find the power factor cos φ of the load.

V = 230 VI = 2.5 AP = 431 W
cos φ =
3.Medium
P = 33 kWQSφ

A single-phase motor takes 33 kW at a power factor of 0.85 lagging from a 400 V supply. Find the line current I.

P = 33 kWpf = 0.85V = 400 V
I = A
4.Medium
P = 2 kWQ = ?Sφ

A single-phase motor takes 2 kW at a power factor of 0.75 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 2 kWpf = 0.75V = 240 V
Q = kvar
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.8 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 20 kWpf1 = 0.8pf2 = 0.92V = 230 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 0.8 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 35 kWpf1 = 0.8pf2 = 0.9V = 240 Vf = 50 Hz
Inew = A

Answer key

  1. 1. cos φ = 0.8742
  2. 2. cos φ = 0.7496
  3. 3. I = 97.06 A
  4. 4. Q = 1.764 kvar
  5. 5. Inew = 94.52 A
  6. 6. Inew = 162 A

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