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 = 470 pF+−12 VL = 10 mHiL​

A 470 pF capacitor charged to 12 V is switched across an ideal 10 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 pFV0 = 12 VL = 10 mH
Imax = mA
2.Easy
C = ?L = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 200 kHz
C = nF
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
V220 Ω22 mH10 pF

A series RLC circuit has R = 220 Ω, L = 22 mH and C = 10 pF. Find its quality factor Q.

R = 220 ΩL = 22 mHC = 10 pF
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 2 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 50 kHzBW = 2 kHz
C = nF
6.Hard
VR = ?47 mHC

A series resonant circuit uses a 47 mH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 47 mHBW = 2 kHz
R = Ω

Answer key

  1. 1. Imax = 2.602 mA
  2. 2. C = 0.1347 nF
  3. 3. t = 10.77 µs
  4. 4. Q = 213.2
  5. 5. C = 1.273 nF
  6. 6. R = 590.6 Ω

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