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 12 A (rms) from a 400 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 400 VI = 12 Apf = cos φ = 0.6
Q = var
2.Easy
240 VloadP = 1092 W6.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 6.5 A and 1092 W. Find the power factor cos φ of the load.

V = 240 VI = 6.5 AP = 1092 W
cos φ =
3.Medium
P = 10 kWQ = ?Sφ

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

P = 10 kWpf = 0.7V = 240 V
Q = kvar
4.Medium
P = 25 kWQSφ

A single-phase motor takes 25 kW at a power factor of 0.85 lagging from a 230 V supply. Find the line current I.

P = 25 kWpf = 0.85V = 230 V
I = A
5.Hard
P1​ = 36 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 36 kW at a power factor of 0.8 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 150 kVAP1 = 36 kWpf1 = 0.8
ΔP = kW
6.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 kW at a power factor of 0.6 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 = 35 kWpf1 = 0.6pf2 = 0.98V = 240 Vf = 60 Hz
Inew = A

Answer key

  1. 1. Q = 3840 var
  2. 2. cos φ = 0.7
  3. 3. Q = 10.2 kvar
  4. 4. I = 127.9 A
  5. 5. ΔP = 111.5 kW
  6. 6. Inew = 148.8 A

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