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 worksheetPractise 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
f|I|0.7071500 kHzf1​f2​BW = ?

A tuned circuit resonates at 500 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 500 kHzQ = 8
BW = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 24 VC = 47 nF

A 47 nF capacitor is charged to 24 V and then connected to an ideal 47 µH inductor. Find the total energy W that swings between them, in µJ.

C = 47 nFV0 = 24 VL = 47 µH
W = µJ
3.Medium
C = 100 nF+−2.25 VL = 470 µHiL​

A 100 nF capacitor charged to 9 V oscillates with an ideal 470 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2.25 V, in µJ.

C = 100 nFV0 = 9 VvC = 2.25 V
WL = µJ
4.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 5
f1 = kHz
5.Hard
C = 1 nFR = 2 ΩL = 47 µH

A charged 1 nF capacitor discharges through a 47 µH coil with a total series resistance of 2 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 = 47 µHC = 1 nFR = 2 Ω
n =
6.Hard
VR = ?4.7 mHC

A series resonant circuit uses a 4.7 mH inductor. Which total series resistance R gives a bandwidth of 5 kHz?

L = 4.7 mHBW = 5 kHz
R = Ω

Answer key

  1. 1. BW = 62.5 kHz
  2. 2. W = 13.54 µJ
  3. 3. WL = 3.797 µJ
  4. 4. f1 = 1.81 kHz
  5. 5. n = 23.92
  6. 6. R = 147.7 Ω

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