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|0.70715 kHzf1​f2​BW = 62.5 Hz

A resonance curve peaks at 5 kHz, and its half-power points are 62.5 Hz apart. Find the quality factor Q.

f0 = 5 kHzBW = 62.5 Hz
Q =
2.Easy
C = 220 nFL = 10 µH

An ideal LC circuit has L = 10 µH and C = 220 nF. Find its natural (resonance) frequency f0 in kHz.

L = 10 µHC = 220 nF
f0 = kHz
3.Medium
V22 kΩ1 mH47 nF

A parallel RLC circuit has R = 22 kΩ, L = 1 mH and C = 47 nF. Find its quality factor Q.

R = 22 kΩL = 1 mHC = 47 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 100 mHC = 2.2 nF

In an ideal LC circuit with L = 100 mH and C = 2.2 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 = 100 mHC = 2.2 nF
t = µs
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 455 kHz and a bandwidth of 11.38 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 455 kHzBW = 11.38 kHz
C = nF
6.Hard
C = 10 µFR = 0.5 ΩL = 2.2 mH

A charged 10 µF capacitor discharges through a 2.2 mH coil with a total series resistance of 0.5 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 = 2.2 mHC = 10 µFR = 0.5 Ω
n =

Answer key

  1. 1. Q = 80
  2. 2. f0 = 107.3 kHz
  3. 3. Q = 150.8
  4. 4. t = 23.3 µs
  5. 5. C = 0.4372 nF
  6. 6. n = 6.545

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