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 load takes 36.5 kW of real power and 11 kvar of reactive power (lagging). Find the apparent power S.

P = 36.5 kWQ = 11 kvar

S = kVA

2.Easy

A load takes 44.5 kW of real power and 49.5 kvar of reactive power (lagging). Find the apparent power S.

P = 44.5 kWQ = 49.5 kvar

S = kVA

3.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 21 kW load at a power factor of 0.6 lagging and a 17 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 400 VP₁ = 21 kW, pf₁ = 0.6 laggingP₂ = 17 kW, pf₂ = 1

I = A

4.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 9 kW load at a power factor of 0.6 lagging and a 17 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 9 kW, pf₁ = 0.6 laggingP₂ = 17 kW, pf₂ = 1

cos φ =

5.Hard

A single-phase load takes 29 kW at a power factor of 0.7 lagging from a 240 V, 60 Hz supply. A 470 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 29 kWpf₁ = 0.7V = 240 Vf = 60 HzC = 470 µF

cos φ =

6.Hard

A single-phase load takes 12 kW at a power factor of 0.7 lagging from a 240 V, 60 Hz supply. A 470 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 12 kWpf₁ = 0.7V = 240 Vf = 60 HzC = 470 µF

cos φ =

Answer key

1. S = 38.12 kVA
2. S = 66.56 kVA
3. I = 118 A
4. cos φ = 0.908
5. cos φ = 0.8314
6. cos φ = 0.9859

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