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
f|I|0.7071455 kHzf1​f2​BW = ?

A tuned circuit resonates at 455 kHz and has a quality factor Q = 10. Find its bandwidth BW in kHz.

f0 = 455 kHzQ = 10
BW = kHz
2.Easy
C = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 10 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 10 kHz
C = nF
3.Medium
V2 Ω1 mH4.7 nF

A series RLC circuit has R = 2 Ω, L = 1 mH and C = 4.7 nF. Find its quality factor Q.

R = 2 ΩL = 1 mHC = 4.7 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 47 µHC = 47 nF

In an ideal LC circuit with L = 47 µH and C = 47 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 = 47 nF
t = µs
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 100 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 100 kHzBW = 5 kHz
C = nF
6.Hard
V10 Ω4.7 mH100 nF10 mA

A series RLC circuit (R = 10 Ω, L = 4.7 mH, C = 100 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 4.7 mHC = 100 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. BW = 45.5 kHz
  2. 2. C = 253.3 nF
  3. 3. Q = 230.6
  4. 4. t = 2.335 µs
  5. 5. C = 1.592 nF
  6. 6. Ecycle = 68.11 nJ

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