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
240 Vload19.5 kW, 21.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 19.5 kW and 21.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 19.5 kWQ = 21.5 kvar
I = A
2.Easy
240 Vload14 kW, 5 kvarI = ?

A single-phase load connected to a 240 V supply takes 14 kW and 5 kvar. Find the current I drawn from the supply.

V = 240 VP = 14 kWQ = 5 kvar
I = A
3.Medium
P = 11 kWQ = ?Sφ

A single-phase motor takes 11 kW at a power factor of 0.8 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 11 kWpf = 0.8V = 240 V
Q = kvar
4.Medium
230 VR + jXP = 2208 W12 A

An inductive load takes 12 A and 2208 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 12 AP = 2208 W
R = Ω
5.Hard
230 V50 Hzload3 kW, 0.7C22 µFI

A single-phase load takes 3 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A 22 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 3 kWpf1 = 0.7V = 230 Vf = 50 HzC = 22 µF
cos φ =
6.Hard
12 V50 HzRs​ = 8 ΩXs​ = j20 ΩZL​ = ?

A 12 V (rms), 50 Hz source has an internal impedance Zs = 8 + j20 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 12 V (rms)f = 50 HzZs = 8 + j20 Ω
Pmax = W

Answer key

  1. 1. I = 120.9 A
  2. 2. I = 61.94 A
  3. 3. Q = 8.25 kvar
  4. 4. R = 15.33 Ω
  5. 5. cos φ = 0.7439
  6. 6. Pmax = 4.5 W

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