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 120 V, 7.5 A and 810 W. Find the power factor cos φ of the load.

V = 120 VI = 7.5 AP = 810 W

cos φ =

2.Easy

A single-phase load draws 12 A (rms) from a 120 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 120 VI = 12 Apf = cos φ = 0.9

P = W

3.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 29 kW load at a power factor of 0.85 lagging and a 30 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 29 kW, pf₁ = 0.85 laggingP₂ = 30 kW, pf₂ = 1

cos φ =

4.Medium

A load with impedance Z = 3 + j4 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 3 + j4 Ω

Q = var

5.Hard

A single-phase load takes 19 kW at a power factor of 0.75 lagging from a 400 V, 50 Hz supply. A 68 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 19 kWpf₁ = 0.75V = 400 Vf = 50 HzC = 68 µF

cos φ =

6.Hard

A single-phase load takes 10 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power Q_C the capacitor must supply.

P = 10 kWpf₁ = 0.65pf₂ = 0.9V = 400 Vf = 50 Hz

Q_C = kvar

Answer key

1. cos φ = 0.9
2. P = 1296 W
3. cos φ = 0.9566
4. Q = 8464 var
5. cos φ = 0.8185
6. Q_C = 6.848 kvar

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