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 20 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 20 Apf = cos φ = 0.6
Q = var
2.Easy
400 Vload15 kW, 19.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 15 kW and 19.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 15 kWQ = 19.5 kvar
I = A
3.Medium
P = 15 kWQ = ?Sφ

A single-phase motor takes 15 kW at a power factor of 0.7 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 15 kWpf = 0.7V = 240 V
Q = kvar
4.Medium
P = 10 kWQSφ

A single-phase motor takes 10 kW at a power factor of 0.6 lagging from a 240 V supply. Find the line current I.

P = 10 kWpf = 0.6V = 240 V
I = A
5.Hard
120 V50 HzRs​ = 20 ΩXs​ = j40 ΩZL​ = ?

A 120 V (rms), 50 Hz source has an internal impedance Zs = 20 + 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 = 120 V (rms)f = 50 HzZs = 20 + j40 Ω
C = µF
6.Hard
50 V1000 HzRs​ = 2 ΩXs​ = j15 ΩZL​ = ?

A 50 V (rms), 1000 Hz source has an internal impedance Zs = 2 + j15 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 = 50 V (rms)f = 1000 HzZs = 2 + j15 Ω
C = µF

Answer key

  1. 1. Q = 3840 var
  2. 2. I = 61.5 A
  3. 3. Q = 15.3 kvar
  4. 4. I = 69.44 A
  5. 5. C = 79.58 µF
  6. 6. C = 10.61 µF

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