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 = 2.2 nF+−24 VL = 4.7 mHiL​

A 2.2 nF capacitor charged to 24 V is switched across an ideal 4.7 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 nFV0 = 24 VL = 4.7 mH
Imax = mA
2.Easy
C = 10 nFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 10 nF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 10 nF
f0 = kHz
3.Medium
tvC​iL​T/4 = ?T/2TL = 47 µHC = 22 nF

In an ideal LC circuit with L = 47 µH and C = 22 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 = 47 µHC = 22 nF
t = µs
4.Medium
V5 Ω220 µH470 pF

A series RLC circuit has R = 5 Ω, L = 220 µH and C = 470 pF. Find its bandwidth BW in kHz.

R = 5 ΩL = 220 µHC = 470 pF
BW = kHz
5.Hard
C = 100 nFR = 2 ΩL = 4.7 mH

A charged 100 nF capacitor discharges through a 4.7 mH 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 = 4.7 mHC = 100 nFR = 2 Ω
n =
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 100 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 100 kHzBW = 2 kHz
C = nF

Answer key

  1. 1. Imax = 16.42 mA
  2. 2. f0 = 73.41 kHz
  3. 3. t = 1.597 µs
  4. 4. BW = 3.617 kHz
  5. 5. n = 23.92
  6. 6. C = 6.366 nF

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