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
C = 470 nFL = 22 mH

An ideal LC circuit has L = 22 mH and C = 470 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 470 nF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 2 VC = 10 nF

A 10 nF capacitor is charged to 2 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in nJ.

C = 10 nFV0 = 2 VL = 47 mH
W = nJ
3.Medium
V2 Ω47 µH470 nF

A series RLC circuit has R = 2 Ω, L = 47 µH and C = 470 nF. Find its quality factor Q.

R = 2 ΩL = 47 µHC = 470 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 mHC = 4.7 nF

In an ideal LC circuit with L = 22 mH and C = 4.7 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 22 mHC = 4.7 nF
t = µs
5.Hard
C = 47 nFR = 0.5 ΩL = 100 µH

A charged 47 nF capacitor discharges through a 100 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 = 100 µHC = 47 nFR = 0.5 Ω
n =
6.Hard
f|I|0.7071f0​ = ?50 kHz80 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 80 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 80 kHz
Q =

Answer key

  1. 1. f0 = 1.565 kHz
  2. 2. W = 20 nJ
  3. 3. Q = 5
  4. 4. t = 15.97 µs
  5. 5. n = 20.35
  6. 6. Q = 2.108

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