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 load takes 35 kW of real power and 28.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 35 kWQ = 28.5 kvar

cos φ =

2.Easy

A single-phase load draws 11 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 = 11 Apf = cos φ = 0.65

P = W

3.Medium

A load with impedance Z = 3 + j4 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 3 + j4 Ω

P = W

4.Medium

Two loads are connected in parallel to a 230 V single-phase supply: a 6 kW load at a power factor of 0.85 lagging and an 18 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 230 VP₁ = 6 kW, pf₁ = 0.85 laggingP₂ = 18 kW, pf₂ = 1

I = A

5.Hard

A single-phase load takes 35 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the reactive power Q_C the capacitor must supply.

P = 35 kWpf₁ = 0.6pf₂ = 0.98V = 400 Vf = 50 Hz

Q_C = kvar

6.Hard

A 200 kVA single-phase transformer supplies a load of 86 kW at a power factor of 0.65 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

S_max = 200 kVAP₁ = 86 kWpf₁ = 0.65

ΔP = kW

Answer key

1. cos φ = 0.7754
2. P = 858 W
3. P = 6912 W
4. I = 105.6 A
5. Q_C = 39.56 kvar
6. ΔP = 86.89 kW

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