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 µFL = 220 µH

An ideal LC circuit has L = 220 µH and C = 2.2 µF. Find its natural (resonance) frequency f0 in kHz.

L = 220 µHC = 2.2 µF
f0 = kHz
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 50. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 50
BW = kHz
3.Medium
V100 Ω47 mH2.2 nF

A series RLC circuit has R = 100 Ω, L = 47 mH and C = 2.2 nF. Find its bandwidth BW in Hz.

R = 100 ΩL = 47 mHC = 2.2 nF
BW = Hz
4.Medium
C = 1 nF+−4 VL = 4.7 mHiL​

A 1 nF capacitor charged to 20 V oscillates with an ideal 4.7 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4 V, in nJ.

C = 1 nFV0 = 20 VvC = 4 V
WL = nJ
5.Hard
VR = ?22 mHC

A series resonant circuit uses a 22 mH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 22 mHBW = 20 kHz
R = Ω
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 500 kHz and a bandwidth of 10 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 500 kHzBW = 10 kHz
C = nF

Answer key

  1. 1. f0 = 7.234 kHz
  2. 2. BW = 214 kHz
  3. 3. BW = 338.6 Hz
  4. 4. WL = 192 nJ
  5. 5. R = 2765 Ω
  6. 6. C = 0.3183 nF

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