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 13 A (rms) from a 400 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 400 VI = 13 Apf = cos φ = 0.8

P = W

2.Easy

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 19.5 A and 1872 W. Find the power factor cos φ of the load.

V = 120 VI = 19.5 AP = 1872 W

cos φ =

3.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 26 kW load at a power factor of 0.75 lagging and a 6 kW heater (unity power factor). Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 26 kW, pf₁ = 0.75 laggingP₂ = 6 kW, pf₂ = 1

cos φ =

4.Medium

An inductive load takes 2.5 A and 431 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 2.5 AP = 431 W

R = Ω

5.Hard

A 150 kVA single-phase transformer supplies a load of 38 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 = 150 kVAP₁ = 38 kWpf₁ = 0.65

ΔP = kW

6.Hard

A single-phase load takes 40 kW at a power factor of 0.75 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current I_new.

P = 40 kWpf₁ = 0.75pf₂ = 0.9V = 400 Vf = 60 Hz

I_new = A

Answer key

1. P = 4160 W
2. cos φ = 0.8
3. cos φ = 0.8129
4. R = 68.96 Ω
5. ΔP = 105.3 kW
6. I_new = 111.1 A

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