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 4 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 120 VI = 4 Apf = cos φ = 0.65
Q = var
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 3 A (rms) from a 230 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 230 VI = 3 Apf = cos φ = 0.65
P = W
3.Medium
240 VZ20 + j15 ΩI

A load with impedance Z = 20 + j15 Ω is connected to a 240 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 240 VZ = 20 + j15 Ω
Q = var
4.Medium
P = 30 kWQ = ?Sφ

A single-phase motor takes 30 kW at a power factor of 0.7 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 30 kWpf = 0.7V = 240 V
Q = kvar
5.Hard
100 V1000 HzRs​ = 2 ΩXs​ = j20 ΩZL​ = ?

A 100 V (rms), 1000 Hz source has an internal impedance Zs = 2 + j20 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 = 1000 HzZs = 2 + j20 Ω
C = µF
6.Hard
P1​ = 16 kWQ1​S1​φ

A 25 kVA single-phase transformer supplies a load of 16 kW at a power factor of 0.85 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 25 kVAP1 = 16 kWpf1 = 0.85
ΔP = kW

Answer key

  1. 1. Q = 364.8 var
  2. 2. P = 448.5 W
  3. 3. Q = 1382 var
  4. 4. Q = 30.61 kvar
  5. 5. C = 7.958 µF
  6. 6. ΔP = 6.949 kW

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