LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth 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 22 nF capacitor is charged to 10 V and then connected to an ideal 2.2 µH inductor. Find the total energy W that swings between them, in µJ.

C = 22 nFV₀ = 10 VL = 2.2 µH

W = µJ

2.Easy

An ideal LC circuit has L = 1 mH and C = 47 pF. Find its natural (resonance) frequency f₀ in kHz.

L = 1 mHC = 47 pF

f₀ = kHz

3.Medium

A parallel RLC circuit has R = 100 kΩ, L = 2.2 mH and C = 1 nF. Find its quality factor Q.

R = 100 kΩL = 2.2 mHC = 1 nF

Q =

4.Medium

A 22 nF capacitor charged to 10 V oscillates with an ideal 4.7 mH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 5 V, in nJ.

C = 22 nFV₀ = 10 Vv_C = 5 V

W_L = nJ

5.Hard

A charged 220 nF capacitor discharges through a 10 µH coil with a total series resistance of 0.5 Ω, so the oscillation slowly dies out. Its amplitude decays as e^−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 10 µHC = 220 nFR = 0.5 Ω

n =

6.Hard

A parallel tank circuit is made of a 100 nF capacitor and a 2.2 mH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance R_D = L/(C·r). Find R_D in kΩ.

L = 2.2 mHC = 100 nFr = 1 Ω

R_D = kΩ

Answer key

1. W = 1.1 µJ
2. f₀ = 734.1 kHz
3. Q = 67.42
4. W_L = 825 nJ
5. n = 2.975
6. R_D = 22 kΩ

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