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 14 A (rms) from a 120 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 120 VI = 14 Apf = cos φ = 0.85

Q = var

2.Easy

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 12 A and 1656 W. Find the reactive power Q taken by the load.

V = 230 VI = 12 AP = 1656 W

Q = var

3.Medium

Two loads are connected in parallel to a 230 V single-phase supply: an 18 kW load at a power factor of 0.8 lagging and a 27 kW load at a power factor of 0.95 leading. Find the overall power factor cos φ seen by the supply.

V = 230 VP₁ = 18 kW, pf₁ = 0.8 laggingP₂ = 27 kW, pf₂ = 0.95 leading

cos φ =

4.Medium

An inductive load takes 13 A and 936 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 = 13 AP = 936 W

R = Ω

5.Hard

A single-phase load takes 40 kW at a power factor of 0.7 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current I_new.

P = 40 kWpf₁ = 0.7pf₂ = 0.9V = 400 Vf = 60 Hz

I_new = A

6.Hard

A single-phase load takes 23 kW at a power factor of 0.6 lagging from a 240 V, 60 Hz supply. A 150 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 23 kWpf₁ = 0.6V = 240 Vf = 60 HzC = 150 µF

I = A

Answer key

1. Q = 885 var
2. Q = 2208 var
3. cos φ = 0.9948
4. R = 5.538 Ω
5. I_new = 111.1 A
6. I = 149.1 A

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