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

A single-phase load draws 11 A (rms) from a 240 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 240 VI = 11 Apf = cos φ = 0.7

Q = var

2.Easy

A single-phase load draws 8 A (rms) from a 230 V (rms) supply at a power factor of 0.7 lagging. Find the real power P it takes.

V = 230 VI = 8 Apf = cos φ = 0.7

P = W

3.Medium

A load with impedance Z = 20 + j15 Ω is connected to a 120 V (rms) single-phase supply. Find the apparent power S.

V = 120 VZ = 20 + j15 Ω

S = VA

4.Medium

Two loads are connected in parallel to a 230 V single-phase supply: a 15 kW load at a power factor of 0.6 lagging and a 25 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 230 VP₁ = 15 kW, pf₁ = 0.6 laggingP₂ = 25 kW, pf₂ = 1

cos φ =

5.Hard

A single-phase load takes 35 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power Q_C the capacitor must supply.

P = 35 kWpf₁ = 0.6pf₂ = 0.9V = 400 Vf = 50 Hz

Q_C = kvar

6.Hard

A single-phase load takes 13 kW at a power factor of 0.6 lagging from a 230 V, 60 Hz supply. A 330 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 13 kWpf₁ = 0.6V = 230 Vf = 60 HzC = 330 µF

I = A

Answer key

1. Q = 1885 var
2. P = 1288 W
3. S = 576 VA
4. cos φ = 0.8944
5. Q_C = 29.72 kvar
6. I = 73.35 A

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