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 Vload26.5 kW, 10.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 26.5 kW and 10.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 26.5 kWQ = 10.5 kvar
I = A
2.Easy
P = 32 kWQ = 20 kvarS = ?φ

A load takes 32 kW of real power and 20 kvar of reactive power (lagging). Find the apparent power S.

P = 32 kWQ = 20 kvar
S = kVA
3.Medium
P = 11 kWQ = ?Sφ

A single-phase motor takes 11 kW at a power factor of 0.75 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 11 kWpf = 0.75V = 230 V
Q = kvar
4.Medium
P = 4 kWQSφ

A single-phase motor takes 4 kW at a power factor of 0.8 lagging from a 240 V supply. Find the line current I.

P = 4 kWpf = 0.8V = 240 V
I = A
5.Hard
230 V50 Hzload29 kW, 0.8C470 µFI

A single-phase load takes 29 kW at a power factor of 0.8 lagging from a 230 V, 50 Hz supply. A 470 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 29 kWpf1 = 0.8V = 230 Vf = 50 HzC = 470 µF
cos φ =
6.Hard
P = 45 kWQ1​S1​φ1​QC​

A single-phase load takes 45 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 capacitance C needed.

P = 45 kWpf1 = 0.75pf2 = 0.98V = 240 Vf = 60 Hz
C = µF

Answer key

  1. 1. I = 71.26 A
  2. 2. S = 37.74 kVA
  3. 3. Q = 9.701 kvar
  4. 4. I = 20.83 A
  5. 5. cos φ = 0.9013
  6. 6. C = 1407 µF

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