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 2 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 2 Apf = cos φ = 0.6
Q = var
2.Easy
120 VloadP = 1728 W18 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 18 A and 1728 W. Find the power factor cos φ of the load.

V = 120 VI = 18 AP = 1728 W
cos φ =
3.Medium
P = 34 kWQSφ

A single-phase motor takes 34 kW at a power factor of 0.65 lagging from a 400 V supply. Find the line current I.

P = 34 kWpf = 0.65V = 400 V
I = A
4.Medium
P = 18 kWQ = ?Sφ

A single-phase motor takes 18 kW at a power factor of 0.65 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 18 kWpf = 0.65V = 240 V
Q = kvar
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 20 kWpf1 = 0.75pf2 = 0.9V = 230 Vf = 50 Hz
C = µF
6.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 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 0.95. Find the new line current Inew.

P = 25 kWpf1 = 0.65pf2 = 0.95V = 400 Vf = 50 Hz
Inew = A

Answer key

  1. 1. Q = 384 var
  2. 2. cos φ = 0.8
  3. 3. I = 130.8 A
  4. 4. Q = 21.04 kvar
  5. 5. C = 478.5 µF
  6. 6. Inew = 65.79 A

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