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
tvC​iL​T/4T/2TV0​ = 10 VC = 2.2 µF

A 2.2 µF capacitor is charged to 10 V and then connected to an ideal 1 µH inductor. Find the total energy W that swings between them, in µJ.

C = 2.2 µFV0 = 10 VL = 1 µH
W = µJ
2.Easy
C = ?L = 47 mH

An LC circuit with L = 47 mH must resonate at 100 kHz. Find the capacitance C in nF.

L = 47 mHf0 = 100 kHz
C = nF
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

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

f0 = 5 kHzQ = 5
f1 = kHz
4.Medium
C = 1 nF+−7.5 VL = 100 mHiL​

A 1 nF capacitor charged to 15 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 7.5 V, in nJ.

C = 1 nFV0 = 15 VvC = 7.5 V
WL = nJ
5.Hard
C = 4.7 nFR = 10 ΩL = 47 µH

A charged 4.7 nF capacitor discharges through a 47 µH coil with a total series resistance of 10 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 = 4.7 nFR = 10 Ω
n =
6.Hard
f|I|0.7071f0​ = ?900 kHz1.8 MHzBW

The half-power frequencies of a resonance curve are 900 kHz and 1.8 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 900 kHzf2 = 1.8 MHz
Q =

Answer key

  1. 1. W = 110 µJ
  2. 2. C = 0.05389 nF
  3. 3. f1 = 4.525 kHz
  4. 4. WL = 84.38 nJ
  5. 5. n = 2.206
  6. 6. Q = 1.414

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