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.

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1.Easy
tvC​iL​T/4T/2TV0​ = 50 VC = 22 nF

A 22 nF capacitor is charged to 50 V and then connected to an ideal 10 mH inductor. Find the total energy W that swings between them, in µJ.

C = 22 nFV0 = 50 VL = 10 mH
W = µJ
2.Easy
C = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 5 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 5 kHz
C = nF
3.Medium
C = 47 nF+−19.2 VL = 1 µHiL​

A 47 nF capacitor charged to 24 V oscillates with an ideal 1 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 19.2 V, in µJ.

C = 47 nFV0 = 24 VvC = 19.2 V
WL = µJ
4.Medium
tvC​iL​T/4 = ?T/2TL = 47 µHC = 1 µF

In an ideal LC circuit with L = 47 µH and C = 1 µF, 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 = 1 µF
t = µs
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 500 Hz. Find the capacitance C in nF.

R = 20 Ωf0 = 10 kHzBW = 500 Hz
C = nF
6.Hard
V1 Ω470 µH22 nF200 mA

A series RLC circuit (R = 1 Ω, L = 470 µH, C = 22 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 470 µHC = 22 nFIm = 200 mA
Ecycle = nJ

Answer key

  1. 1. W = 27.5 µJ
  2. 2. C = 1013 nF
  3. 3. WL = 4.873 µJ
  4. 4. t = 10.77 µs
  5. 5. C = 39.79 nF
  6. 6. Ecycle = 404.1 nJ

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