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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A single-phase load draws 19 A (rms) from a 230 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 230 VI = 19 Apf = cos φ = 0.65

Q = var

2.Easy

A load takes 33 kW of real power and 27 kvar of reactive power (lagging). Find the power factor cos φ.

P = 33 kWQ = 27 kvar

cos φ =

3.Medium

Two loads are connected in parallel to a 240 V single-phase supply: a 9 kW load at a power factor of 0.85 lagging and a 12 kW load at a power factor of 0.7 lagging. Find the total current I drawn from the supply.

V = 240 VP₁ = 9 kW, pf₁ = 0.85 laggingP₂ = 12 kW, pf₂ = 0.7 lagging

I = A

4.Medium

An inductive load takes 11.5 A and 828 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 11.5 AP = 828 W

X = Ω

5.Hard

A single-phase load takes 30 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 capacitance C needed.

P = 30 kWpf₁ = 0.65pf₂ = 0.9V = 400 Vf = 50 Hz

C = µF

6.Hard

A 25 kVA single-phase transformer supplies a load of 13 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 = 25 kVAP₁ = 13 kWpf₁ = 0.65

ΔP = kW

Answer key

1. Q = 3321 var
2. cos φ = 0.774
3. I = 114.8 A
4. X = 8.348 Ω
5. C = 408.7 µF
6. ΔP = 6.849 kW

Full step-by-step solutions: practise this topic on examproblems.com.