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​ = 12 VC = 220 nF

A 220 nF capacitor is charged to 12 V and then connected to an ideal 0.47 µH inductor. Find the total energy W that swings between them, in µJ.

C = 220 nFV0 = 12 VL = 0.47 µH
W = µJ
2.Easy
f|I|0.7071100 kHzf1​f2​BW = ?

A tuned circuit resonates at 100 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 100 kHzQ = 8
BW = kHz
3.Medium
V22 kΩ470 µH470 pF

A parallel RLC circuit has R = 22 kΩ, L = 470 µH and C = 470 pF. Find its quality factor Q.

R = 22 kΩL = 470 µHC = 470 pF
Q =
4.Medium
V5 Ω10 µH100 nF

A series RLC circuit has R = 5 Ω, L = 10 µH and C = 100 nF. Find its bandwidth BW in kHz.

R = 5 ΩL = 10 µHC = 100 nF
BW = kHz
5.Hard
C = 47 nFR = 10 ΩL = 47 mH

A charged 47 nF capacitor discharges through a 47 mH coil with a total series resistance of 10 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 = 47 mHC = 47 nFR = 10 Ω
n =
6.Hard
V2 Ω1 mH4.7 nF50 mA

A series RLC circuit (R = 2 Ω, L = 1 mH, C = 4.7 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 1 mHC = 4.7 nFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. W = 15.84 µJ
  2. 2. BW = 12.5 kHz
  3. 3. Q = 22
  4. 4. BW = 79.58 kHz
  5. 5. n = 22.06
  6. 6. Ecycle = 34.05 nJ

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