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
C = 47 nFL = 0.47 µH

An ideal LC circuit has L = 0.47 µH and C = 47 nF. Find its natural (resonance) frequency f0 in MHz.

L = 0.47 µHC = 47 nF
f0 = MHz
2.Easy
tvC​iL​T/4T/2TV0​ = 5 VC = 470 nF

A 470 nF capacitor is charged to 5 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in µJ.

C = 470 nFV0 = 5 VL = 1 mH
W = µJ
3.Medium
C = 2.2 nF+−6 VL = 1 mHiL​

A 2.2 nF capacitor charged to 24 V oscillates with an ideal 1 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in nJ.

C = 2.2 nFV0 = 24 VvC = 6 V
WL = nJ
4.Medium
V47 Ω220 µH1 nF

A series RLC circuit has R = 47 Ω, L = 220 µH and C = 1 nF. Find its bandwidth BW in kHz.

R = 47 ΩL = 220 µHC = 1 nF
BW = kHz
5.Hard
V10 Ω22 mH10 nF10 mA

A series RLC circuit (R = 10 Ω, L = 22 mH, C = 10 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 22 mHC = 10 nFIm = 10 mA
Ecycle = nJ
6.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

Answer key

  1. 1. f0 = 1.071 MHz
  2. 2. W = 5.875 µJ
  3. 3. WL = 594 nJ
  4. 4. BW = 34 kHz
  5. 5. Ecycle = 46.6 nJ
  6. 6. C = 39.79 nF

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