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
tvC​iL​T/4T/2TV0​ = 2 VC = 10 µF

A 10 µF capacitor is charged to 2 V and then connected to an ideal 10 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 2 VL = 10 µH
W = µJ
2.Easy
C = 2.2 µF+−3 VL = 4.7 mHiL​

A 2.2 µF capacitor charged to 3 V is switched across an ideal 4.7 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 µFV0 = 3 VL = 4.7 mH
Imax = mA
3.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 5
f1 = kHz
4.Medium
V2 Ω22 µH10 nF

A series RLC circuit has R = 2 Ω, L = 22 µH and C = 10 nF. Find its quality factor Q.

R = 2 ΩL = 22 µHC = 10 nF
Q =
5.Hard
V10 ΩLC = ?

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

R = 10 Ωf0 = 10 kHzBW = 400 Hz
C = nF
6.Hard
C = 100 pFR = 20 ΩL = 4.7 mH

A charged 100 pF capacitor discharges through a 4.7 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 = 4.7 mHC = 100 pFR = 20 Ω
n =

Answer key

  1. 1. W = 20 µJ
  2. 2. Imax = 64.91 mA
  3. 3. f1 = 90.5 kHz
  4. 4. Q = 23.45
  5. 5. C = 63.66 nF
  6. 6. n = 75.63

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