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 13 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 400 VI = 13 Apf = cos φ = 0.9

Q = var

2.Easy

A load takes 44.5 kW of real power and 50 kvar of reactive power (lagging). Find the apparent power S.

P = 44.5 kWQ = 50 kvar

S = kVA

3.Medium

An inductive load takes 12.5 A and 1725 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 12.5 AP = 1725 W

X = Ω

4.Medium

Two loads are connected in parallel to a 240 V single-phase supply: a 7 kW load at a power factor of 0.7 lagging and a 15 kW load at a power factor of 0.8 lagging. Find the total current I drawn from the supply.

V = 240 VP₁ = 7 kW, pf₁ = 0.7 laggingP₂ = 15 kW, pf₂ = 0.8 lagging

I = A

5.Hard

A single-phase load takes 15 kW at a power factor of 0.8 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current I_new.

P = 15 kWpf₁ = 0.8pf₂ = 0.95V = 230 Vf = 50 Hz

I_new = A

6.Hard

A single-phase load takes 10 kW at a power factor of 0.7 lagging from a 400 V, 60 Hz supply. A 47 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 10 kWpf₁ = 0.7V = 400 Vf = 60 HzC = 47 µF

cos φ =

Answer key

1. Q = 2267 var
2. S = 66.93 kVA
3. X = 14.72 Ω
4. I = 119.5 A
5. I_new = 68.65 A
6. cos φ = 0.8051

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