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
400 Vload5.5 kW, 4.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 5.5 kW and 4.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 5.5 kWQ = 4.5 kvar
I = A
2.Easy
120 VloadP = 360 W5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 5 A and 360 W. Find the power factor cos φ of the load.

V = 120 VI = 5 AP = 360 W
cos φ =
3.Medium
P = 10 kWQ = ?Sφ

A single-phase motor takes 10 kW at a power factor of 0.85 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 10 kWpf = 0.85V = 400 V
Q = kvar
4.Medium
P = 28 kWQSφ

A single-phase motor takes 28 kW at a power factor of 0.6 lagging from a 230 V supply. Find the line current I.

P = 28 kWpf = 0.6V = 230 V
I = A
5.Hard
P1​ = 26 kWQ1​S1​φ

A 75 kVA single-phase transformer supplies a load of 26 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 = 75 kVAP1 = 26 kWpf1 = 0.8
ΔP = kW
6.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.8 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 15 kWpf1 = 0.8pf2 = 0.95V = 230 Vf = 60 Hz
C = µF

Answer key

  1. 1. I = 17.77 A
  2. 2. cos φ = 0.6
  3. 3. Q = 6.197 kvar
  4. 4. I = 202.9 A
  5. 5. ΔP = 46.42 kW
  6. 6. C = 316.9 µF

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