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
240 VloadP = 2856 W14 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 14 A and 2856 W. Find the power factor cos φ of the load.

V = 240 VI = 14 AP = 2856 W
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 9 A (rms) from a 120 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 120 VI = 9 Apf = cos φ = 0.8
Q = var
3.Medium
P = 25 kWQSφ

A single-phase motor takes 25 kW at a power factor of 0.8 lagging from a 240 V supply. Find the line current I.

P = 25 kWpf = 0.8V = 240 V
I = A
4.Medium
P = 33 kWQ = ?Sφ

A single-phase motor takes 33 kW at a power factor of 0.8 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 33 kWpf = 0.8V = 240 V
Q = kvar
5.Hard
P = 25 kWQ1​S1​φ1​QC​

A single-phase load takes 25 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 0.95. Find the capacitance C needed.

P = 25 kWpf1 = 0.7pf2 = 0.95V = 240 Vf = 50 Hz
C = µF
6.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 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 0.98. Find the new line current Inew.

P = 15 kWpf1 = 0.75pf2 = 0.98V = 240 Vf = 60 Hz
Inew = A

Answer key

  1. 1. cos φ = 0.85
  2. 2. Q = 648 var
  3. 3. I = 130.2 A
  4. 4. Q = 24.75 kvar
  5. 5. C = 955.4 µF
  6. 6. Inew = 63.78 A

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