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 voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 18.5 A and 3330 W. Find the power factor cos φ of the load.

V = 240 VI = 18.5 AP = 3330 W

cos φ =

2.Easy

A single-phase load draws 20 A (rms) from a 240 V (rms) supply at a power factor of 0.75 lagging. Find the real power P it takes.

V = 240 VI = 20 Apf = cos φ = 0.75

P = W

3.Medium

A single-phase motor takes 11 kW at a power factor of 0.6 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 11 kWpf = 0.6V = 240 V

Q = kvar

4.Medium

An inductive load takes 2.5 A and 345 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 2.5 AP = 345 W

R = Ω

5.Hard

A 200 kVA single-phase transformer supplies a load of 97 kW at a power factor of 0.75 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

S_max = 200 kVAP₁ = 97 kWpf₁ = 0.75

ΔP = kW

6.Hard

A single-phase load takes 9 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A 150 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 9 kWpf₁ = 0.75V = 230 Vf = 50 HzC = 150 µF

cos φ =

Answer key

1. cos φ = 0.75
2. P = 3600 W
3. Q = 14.67 kvar
4. R = 55.2 Ω
5. ΔP = 83.78 kW
6. cos φ = 0.8556

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