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 6 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 120 VI = 6 Apf = cos φ = 0.65

P = W

2.Easy

A load takes 16.5 kW of real power and 6.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 16.5 kWQ = 6.5 kvar

cos φ =

3.Medium

Two loads are connected in parallel to a 240 V single-phase supply: a 21 kW load at a power factor of 0.85 lagging and a 16 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 240 VP₁ = 21 kW, pf₁ = 0.85 laggingP₂ = 16 kW, pf₂ = 1

I = A

4.Medium

A load with impedance Z = 12 + j16 Ω is connected to a 240 V (rms) single-phase supply. Find the apparent power S.

V = 240 VZ = 12 + j16 Ω

S = VA

5.Hard

A single-phase load takes 27 kW at a power factor of 0.6 lagging from a 240 V, 60 Hz supply. A 330 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 27 kWpf₁ = 0.6V = 240 Vf = 60 HzC = 330 µF

cos φ =

6.Hard

A single-phase load takes 9 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 line current I.

P = 9 kWpf₁ = 0.7V = 400 Vf = 60 HzC = 47 µF

I = A

Answer key

1. P = 468 W
2. cos φ = 0.9304
3. I = 163.4 A
4. S = 2880 VA
5. cos φ = 0.6835
6. I = 27.53 A

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