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
120 Vload26 kW, 18 kvarI = ?

A single-phase load connected to a 120 V supply takes 26 kW and 18 kvar. Find the current I drawn from the supply.

V = 120 VP = 26 kWQ = 18 kvar
I = A
2.Easy
P = 37.5 kWQ = 24.5 kvarSφ

A load takes 37.5 kW of real power and 24.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 37.5 kWQ = 24.5 kvar
cos φ =
3.Medium
P = 23 kWQ = ?Sφ

A single-phase motor takes 23 kW at a power factor of 0.85 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 23 kWpf = 0.85V = 240 V
Q = kvar
4.Medium
P = 32 kWQ = ?Sφ

A single-phase motor takes 32 kW at a power factor of 0.65 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 32 kWpf = 0.65V = 230 V
Q = kvar
5.Hard
400 V50 Hzload29 kW, 0.7C100 µFI

A single-phase load takes 29 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A 100 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 29 kWpf1 = 0.7V = 400 Vf = 50 HzC = 100 µF
cos φ =
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.6 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 = 5 kWpf1 = 0.6pf2 = 0.95V = 240 Vf = 50 Hz
C = µF

Answer key

  1. 1. I = 263.5 A
  2. 2. cos φ = 0.8372
  3. 3. Q = 14.25 kvar
  4. 4. Q = 37.41 kvar
  5. 5. cos φ = 0.7631
  6. 6. C = 277.6 µF

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