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 42 kW of real power and 39.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 42 kWQ = 39.5 kvar

cos φ =

2.Easy

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 7.5 A and 720 W. Find the power factor cos φ of the load.

V = 120 VI = 7.5 AP = 720 W

cos φ =

3.Medium

Two loads are connected in parallel to a 240 V single-phase supply: a 14 kW load at a power factor of 0.85 lagging and a 2 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 240 VP₁ = 14 kW, pf₁ = 0.85 laggingP₂ = 2 kW, pf₂ = 1

I = A

4.Medium

A load with impedance Z = 4 + j3 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 4 + j3 Ω

P = W

5.Hard

A 75 kVA single-phase transformer supplies a load of 21 kW at a power factor of 0.6 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 = 75 kVAP₁ = 21 kWpf₁ = 0.6

ΔP = kW

6.Hard

A single-phase load takes 17 kW at a power factor of 0.65 lagging from a 230 V, 60 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 = 17 kWpf₁ = 0.65V = 230 Vf = 60 HzC = 150 µF

cos φ =

Answer key

1. cos φ = 0.7285
2. cos φ = 0.8
3. I = 75.84 A
4. P = 9216 W
5. ΔP = 48.58 kW
6. cos φ = 0.7095

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