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 load takes 23.5 kW of real power and 28 kvar of reactive power (lagging). Find the power factor cos φ.

P = 23.5 kWQ = 28 kvar

cos φ =

2.Easy

A single-phase load draws 9 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 240 VI = 9 Apf = cos φ = 0.85

P = W

3.Medium

A single-phase motor takes 13 kW at a power factor of 0.6 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 13 kWpf = 0.6V = 400 V

Q = kvar

4.Medium

An inductive load takes 19.5 A and 1638 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 = 19.5 AP = 1638 W

X = Ω

5.Hard

A single-phase load takes 20 kW at a power factor of 0.75 lagging from a 240 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 = 20 kWpf₁ = 0.75pf₂ = 0.98V = 240 Vf = 50 Hz

Q_C = kvar

6.Hard

A 230 V (rms), 60 Hz source has an internal impedance Z_s = 10 + j5 Ω. The load impedance Z_L can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

V_s = 230 V (rms)f = 60 HzZ_s = 10 + j5 Ω

C = µF

Answer key

1. cos φ = 0.6429
2. P = 1836 W
3. Q = 17.33 kvar
4. X = 4.395 Ω
5. Q_C = 13.58 kvar
6. C = 530.5 µF

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