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 = ?L = 47 µH

An LC circuit with L = 47 µH must resonate at 455 kHz. Find the capacitance C in nF.

L = 47 µHf0 = 455 kHz
C = nF
2.Easy
C = 100 nFL = 220 µH

An ideal LC circuit has L = 220 µH and C = 100 nF. Find its natural (resonance) frequency f0 in kHz.

L = 220 µHC = 100 nF
f0 = kHz
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 1.5
f1 = Hz
4.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 1.5
f1 = kHz
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 500 kHz and a bandwidth of 10 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 500 kHzBW = 10 kHz
C = nF
6.Hard
C = 22 nFR = 20 ΩL = 1 mH

A charged 22 nF capacitor discharges through a 1 mH coil with a total series resistance of 20 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 = 1 mHC = 22 nFR = 20 Ω
n =

Answer key

  1. 1. C = 2.603 nF
  2. 2. f0 = 33.93 kHz
  3. 3. f1 = 720.8 Hz
  4. 4. f1 = 1.442 kHz
  5. 5. C = 0.1273 nF
  6. 6. n = 2.352

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