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 18 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 240 VI = 18 Apf = cos φ = 0.85
Q = var
2.Easy
120 Vload27.5 kW, 17.5 kvarI = ?

A single-phase load connected to a 120 V supply takes 27.5 kW and 17.5 kvar. Find the current I drawn from the supply.

V = 120 VP = 27.5 kWQ = 17.5 kvar
I = A
3.Medium
P = 25 kWQSφ

A single-phase motor takes 25 kW at a power factor of 0.65 lagging from a 240 V supply. Find the line current I.

P = 25 kWpf = 0.65V = 240 V
I = A
4.Medium
P = 31 kWQSφ

A single-phase motor takes 31 kW at a power factor of 0.7 lagging from a 230 V supply. Find the line current I.

P = 31 kWpf = 0.7V = 230 V
I = A
5.Hard
230 V50 Hzload29 kW, 0.6C330 µFI = ?

A single-phase load takes 29 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A 330 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 29 kWpf1 = 0.6V = 230 Vf = 50 HzC = 330 µF
I = A
6.Hard
10 V50 HzRs​ = 8 ΩXs​ = j3 ΩZL​ = ?

A 10 V (rms), 50 Hz source has an internal impedance Zs = 8 + j3 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 = 10 V (rms)f = 50 HzZs = 8 + j3 Ω
C = µF

Answer key

  1. 1. Q = 2276 var
  2. 2. I = 271.6 A
  3. 3. I = 160.3 A
  4. 4. I = 192.5 A
  5. 5. I = 191.6 A
  6. 6. C = 1061 µF

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