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 230 V, 2 A and 299 W. Find the power factor cos φ of the load.

V = 230 VI = 2 AP = 299 W

cos φ =

2.Easy

A single-phase load connected to a 120 V supply takes 17.5 kW and 10 kvar. Find the current I drawn from the supply.

V = 120 VP = 17.5 kWQ = 10 kvar

I = A

3.Medium

An inductive load takes 19 A and 2052 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 120 VI = 19 AP = 2052 W

R = Ω

4.Medium

A load with impedance Z = 12 + j5 Ω is connected to a 230 V (rms) single-phase supply. Find the real power P it absorbs.

V = 230 VZ = 12 + j5 Ω

P = W

5.Hard

A single-phase load takes 15 kW at a power factor of 0.65 lagging from a 400 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 = 15 kWpf₁ = 0.65V = 400 Vf = 60 HzC = 150 µF

cos φ =

6.Hard

A 50 kVA single-phase transformer supplies a load of 26 kW at a power factor of 0.7 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 = 50 kVAP₁ = 26 kWpf₁ = 0.7

ΔP = kW

Answer key

1. cos φ = 0.65
2. I = 168 A
3. R = 5.684 Ω
4. P = 3756 W
5. cos φ = 0.8703
6. ΔP = 16.38 kW

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