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 Vload2.5 kW, 2.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 2.5 kW and 2.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 2.5 kWQ = 2.5 kvar
I = A
2.Easy
P = 33 kWQ = 42 kvarSφ

A load takes 33 kW of real power and 42 kvar of reactive power (lagging). Find the power factor cos φ.

P = 33 kWQ = 42 kvar
cos φ =
3.Medium
240 VR + jXP = 2160 W18 A

An inductive load takes 18 A and 2160 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 240 VI = 18 AP = 2160 W
X = Ω
4.Medium
P = 6 kWQ = ?Sφ

A single-phase motor takes 6 kW at a power factor of 0.7 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 6 kWpf = 0.7V = 240 V
Q = kvar
5.Hard
400 V60 Hzload12 kW, 0.7C150 µFI = ?

A single-phase load takes 12 kW at a power factor of 0.7 lagging from a 400 V, 60 Hz supply. A 150 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 12 kWpf1 = 0.7V = 400 Vf = 60 HzC = 150 µF
I = A
6.Hard
230 V60 HzRs​ = 20 ΩXs​ = j30 ΩZL​ = ?

A 230 V (rms), 60 Hz source has an internal impedance Zs = 20 + j30 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 230 V (rms)f = 60 HzZs = 20 + j30 Ω
Pmax = W

Answer key

  1. 1. I = 14.73 A
  2. 2. cos φ = 0.6178
  3. 3. X = 11.55 Ω
  4. 4. Q = 6.121 kvar
  5. 5. I = 31.04 A
  6. 6. Pmax = 661.3 W

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