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 = 18 kWQ = 14.5 kvarSφ

A load takes 18 kW of real power and 14.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 18 kWQ = 14.5 kvar
cos φ =
2.Easy
240 VloadP = 3978 W19.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 19.5 A and 3978 W. Find the power factor cos φ of the load.

V = 240 VI = 19.5 AP = 3978 W
cos φ =
3.Medium
P = 36 kWQSφ

A single-phase motor takes 36 kW at a power factor of 0.8 lagging from a 400 V supply. Find the line current I.

P = 36 kWpf = 0.8V = 400 V
I = A
4.Medium
120 VZ3 + j4 ΩI

A load with impedance Z = 3 + j4 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 3 + j4 Ω
Q = var
5.Hard
P = 10 kWQ1​S1​φ1​QC​

A single-phase load takes 10 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 = 10 kWpf1 = 0.75pf2 = 0.98V = 240 Vf = 60 Hz
Inew = A
6.Hard
230 V50 Hzload28 kW, 0.75C470 µFI = ?

A single-phase load takes 28 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A 470 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 28 kWpf1 = 0.75V = 230 Vf = 50 HzC = 470 µF
I = A

Answer key

  1. 1. cos φ = 0.7788
  2. 2. cos φ = 0.85
  3. 3. I = 112.5 A
  4. 4. Q = 2304 var
  5. 5. Inew = 42.52 A
  6. 6. I = 142.2 A

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