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 = 10 nF+−6 VL = 470 µHiL​

A 10 nF capacitor charged to 6 V is switched across an ideal 470 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 10 nFV0 = 6 VL = 470 µH
Imax = mA
2.Easy
tvC​iL​T/4T/2TV0​ = 3 VC = 4.7 nF

A 4.7 nF capacitor is charged to 3 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in nJ.

C = 4.7 nFV0 = 3 VL = 4.7 mH
W = nJ
3.Medium
V10 Ω47 µH2.2 nF

A series RLC circuit has R = 10 Ω, L = 47 µH and C = 2.2 nF. Find its quality factor Q.

R = 10 ΩL = 47 µHC = 2.2 nF
Q =
4.Medium
C = 1 nF+−6 VL = 470 µHiL​

A 1 nF capacitor charged to 15 V oscillates with an ideal 470 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in nJ.

C = 1 nFV0 = 15 VvC = 6 V
WL = nJ
5.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 20 kHz and a bandwidth of 400 Hz. Find the capacitance C in nF.

R = 10 Ωf0 = 20 kHzBW = 400 Hz
C = nF
6.Hard
VR = ?22 mHC

A series resonant circuit uses a 22 mH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 22 mHBW = 10 kHz
R = Ω

Answer key

  1. 1. Imax = 27.68 mA
  2. 2. W = 21.15 nJ
  3. 3. Q = 14.62
  4. 4. WL = 94.5 nJ
  5. 5. C = 15.92 nF
  6. 6. R = 1382 Ω

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