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 connected to a 120 V supply takes 25 kW and 8.5 kvar. Find the current I drawn from the supply.

V = 120 VP = 25 kWQ = 8.5 kvar

I = A

2.Easy

A single-phase load draws 4 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 4 Apf = cos φ = 0.6

Q = var

3.Medium

An inductive load takes 7.5 A and 1380 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 = 7.5 AP = 1380 W

R = Ω

4.Medium

An inductive load takes 20 A and 4080 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 240 VI = 20 AP = 4080 W

X = Ω

5.Hard

A single-phase load takes 40 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current I_new.

P = 40 kWpf₁ = 0.8pf₂ = 0.95V = 400 Vf = 60 Hz

I_new = A

6.Hard

A single-phase load takes 22 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 22 kWpf₁ = 0.6V = 230 Vf = 50 HzC = 220 µF

cos φ =

Answer key

1. I = 220 A
2. Q = 768 var
3. R = 24.53 Ω
4. X = 6.321 Ω
5. I_new = 105.3 A
6. cos φ = 0.6506

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