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
P = 18.5 kWQ = 6.5 kvarSφ

A load takes 18.5 kW of real power and 6.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 18.5 kWQ = 6.5 kvar
cos φ =
2.Easy
P = 45.5 kWQ = 29.5 kvarS = ?φ

A load takes 45.5 kW of real power and 29.5 kvar of reactive power (lagging). Find the apparent power S.

P = 45.5 kWQ = 29.5 kvar
S = kVA
3.Medium
120 VZ4 + j3 ΩI

A load with impedance Z = 4 + j3 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 4 + j3 Ω
Q = var
4.Medium
P = 11 kWQ = ?Sφ

A single-phase motor takes 11 kW at a power factor of 0.6 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 11 kWpf = 0.6V = 240 V
Q = kvar
5.Hard
240 V60 Hzload14 kW, 0.6C150 µFI

A single-phase load takes 14 kW at a power factor of 0.6 lagging from a 240 V, 60 Hz supply. A 150 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 14 kWpf1 = 0.6V = 240 Vf = 60 HzC = 150 µF
cos φ =
6.Hard
230 V50 HzRs​ = 10 ΩXs​ = j40 ΩZL​ = ?

A 230 V (rms), 50 Hz source has an internal impedance Zs = 10 + j40 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 = 50 HzZs = 10 + j40 Ω
Pmax = W

Answer key

  1. 1. cos φ = 0.9435
  2. 2. S = 54.23 kVA
  3. 3. Q = 1728 var
  4. 4. Q = 14.67 kvar
  5. 5. cos φ = 0.6724
  6. 6. Pmax = 1323 W

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