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
PQ = ?S = V·Iφ

A single-phase load draws 17 A (rms) from a 120 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 120 VI = 17 Apf = cos φ = 0.95
Q = var
2.Easy
240 Vload27 kW, 18.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 27 kW and 18.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 27 kWQ = 18.5 kvar
I = A
3.Medium
P = 8 kWQSφ

A single-phase motor takes 8 kW at a power factor of 0.65 lagging from a 240 V supply. Find the line current I.

P = 8 kWpf = 0.65V = 240 V
I = A
4.Medium
P = 1 kWQ = ?Sφ

A single-phase motor takes 1 kW at a power factor of 0.85 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 1 kWpf = 0.85V = 230 V
Q = kvar
5.Hard
240 V60 Hzload28 kW, 0.65C330 µFI

A single-phase load takes 28 kW at a power factor of 0.65 lagging from a 240 V, 60 Hz supply. A 330 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 28 kWpf1 = 0.65V = 240 Vf = 60 HzC = 330 µF
cos φ =
6.Hard
100 V50 HzRs​ = 50 ΩXs​ = j40 ΩZL​ = ?

A 100 V (rms), 50 Hz source has an internal impedance Zs = 50 + j40 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 100 V (rms)f = 50 HzZs = 50 + j40 Ω
C = µF

Answer key

  1. 1. Q = 637 var
  2. 2. I = 136.4 A
  3. 3. I = 51.28 A
  4. 4. Q = 0.6197 kvar
  5. 5. cos φ = 0.7384
  6. 6. C = 79.58 µF

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