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
f|I|0.70711 kHzf1​f2​BW = 25 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 25 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 25 Hz
Q =
2.Easy
C = 22 nFL = 10 µH

An ideal LC circuit has L = 10 µH and C = 22 nF. Find its natural (resonance) frequency f0 in kHz.

L = 10 µHC = 22 nF
f0 = kHz
3.Medium
tvC​iL​T/4 = ?T/2TL = 47 mHC = 1 nF

In an ideal LC circuit with L = 47 mH and C = 1 nF, 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 mHC = 1 nF
t = µs
4.Medium
C = 10 nF+−2 VL = 100 mHiL​

A 10 nF capacitor charged to 5 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2 V, in nJ.

C = 10 nFV0 = 5 VvC = 2 V
WL = nJ
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 20 kHz and a bandwidth of 800 Hz. Find the capacitance C in nF.

R = 20 Ωf0 = 20 kHzBW = 800 Hz
C = nF
6.Hard
VR = ?10 µHC

A series resonant circuit uses a 10 µH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 10 µHBW = 20 kHz
R = Ω

Answer key

  1. 1. Q = 40
  2. 2. f0 = 339.3 kHz
  3. 3. t = 10.77 µs
  4. 4. WL = 105 nJ
  5. 5. C = 15.92 nF
  6. 6. R = 1.257 Ω

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