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 18 A (rms) from a 230 V (rms) supply at a power factor of 0.6 lagging. Find the real power P it takes.

V = 230 VI = 18 Apf = cos φ = 0.6

P = W

2.Easy

A load takes 48 kW of real power and 32 kvar of reactive power (lagging). Find the power factor cos φ.

P = 48 kWQ = 32 kvar

cos φ =

3.Medium

A single-phase motor takes 39 kW at a power factor of 0.8 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 39 kWpf = 0.8V = 240 V

Q = kvar

4.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 12 kW load at a power factor of 0.75 lagging and a 29 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 12 kW, pf₁ = 0.75 laggingP₂ = 29 kW, pf₂ = 1

cos φ =

5.Hard

A single-phase load takes 50 kW at a power factor of 0.65 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 50 kWpf₁ = 0.65pf₂ = 0.95V = 230 Vf = 50 Hz

C = µF

6.Hard

A single-phase load takes 30 kW at a power factor of 0.75 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 30 kWpf₁ = 0.75pf₂ = 0.95V = 240 Vf = 60 Hz

C = µF

Answer key

1. P = 2484 W
2. cos φ = 0.8321
3. Q = 29.25 kvar
4. cos φ = 0.9683
5. C = 2529 µF
6. C = 764.3 µF

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