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 = 100 nFL = 10 µH

An ideal LC circuit has L = 10 µH and C = 100 nF. Find its natural (resonance) frequency f0 in kHz.

L = 10 µHC = 100 nF
f0 = kHz
2.Easy
C = ?L = 100 µH

An LC circuit with L = 100 µH must resonate at 100 kHz. Find the capacitance C in nF.

L = 100 µHf0 = 100 kHz
C = nF
3.Medium
C = 4.7 nF+−4 VL = 22 µHiL​

A 4.7 nF capacitor charged to 20 V oscillates with an ideal 22 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4 V, in nJ.

C = 4.7 nFV0 = 20 VvC = 4 V
WL = nJ
4.Medium
V10 kΩ2.2 mH220 nF

A parallel RLC circuit has R = 10 kΩ, L = 2.2 mH and C = 220 nF. Find its quality factor Q.

R = 10 kΩL = 2.2 mHC = 220 nF
Q =
5.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 50 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 50 kHzBW = 5 kHz
C = nF
6.Hard
VR = ?2.2 mHC

A series resonant circuit uses a 2.2 mH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 2.2 mHBW = 1 kHz
R = Ω

Answer key

  1. 1. f0 = 159.2 kHz
  2. 2. C = 25.33 nF
  3. 3. WL = 902.4 nJ
  4. 4. Q = 100
  5. 5. C = 3.183 nF
  6. 6. R = 13.82 Ω

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