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 16 A (rms) from a 240 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 240 VI = 16 Apf = cos φ = 0.9

Q = var

2.Easy

A single-phase load draws 10 A (rms) from a 400 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 400 VI = 10 Apf = cos φ = 0.8

P = W

3.Medium

A load with impedance Z = 9 + j12 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 9 + j12 Ω

Q = var

4.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 16 kW load at a power factor of 0.65 lagging and a 26 kW load at a power factor of 0.7 leading. Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 16 kW, pf₁ = 0.65 laggingP₂ = 26 kW, pf₂ = 0.7 leading

cos φ =

5.Hard

A single-phase load takes 10 kW at a power factor of 0.6 lagging from a 230 V, 60 Hz supply. A 68 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 10 kWpf₁ = 0.6V = 230 Vf = 60 HzC = 68 µF

I = A

6.Hard

A single-phase load takes 50 kW at a power factor of 0.8 lagging from a 400 V, 60 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 = 50 kWpf₁ = 0.8pf₂ = 0.9V = 400 Vf = 60 Hz

Q_C = kvar

Answer key

1. Q = 1674 var
2. P = 3200 W
3. Q = 2821 var
4. cos φ = 0.9831
5. I = 67.84 A
6. Q_C = 13.28 kvar

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