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 = 1 µFL = 1 mH

An ideal LC circuit has L = 1 mH and C = 1 µF. Find its natural (resonance) frequency f0 in kHz.

L = 1 mHC = 1 µF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 1 VC = 4.7 nF

A 4.7 nF capacitor is charged to 1 V and then connected to an ideal 100 mH inductor. Find the total energy W that swings between them, in nJ.

C = 4.7 nFV0 = 1 VL = 100 mH
W = nJ
3.Medium
tvC​iL​T/4 = ?T/2TL = 22 µHC = 10 µF

In an ideal LC circuit with L = 22 µH and C = 10 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 = 22 µHC = 10 µF
t = µs
4.Medium
V1 kΩ470 µH47 nF

A parallel RLC circuit has R = 1 kΩ, L = 470 µH and C = 47 nF. Find its quality factor Q.

R = 1 kΩL = 470 µHC = 47 nF
Q =
5.Hard
V2 Ω220 µH22 nF10 mA

A series RLC circuit (R = 2 Ω, L = 220 µH, C = 22 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 = 2 ΩL = 220 µHC = 22 nFIm = 10 mA
Ecycle = nJ
6.Hard
C = 10 nFR = 10 ΩL = 47 µH

A charged 10 nF capacitor discharges through a 47 µH coil with a total series resistance of 10 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 47 µHC = 10 nFR = 10 Ω
n =

Answer key

  1. 1. f0 = 5.033 kHz
  2. 2. W = 2.35 nJ
  3. 3. t = 23.3 µs
  4. 4. Q = 10
  5. 5. Ecycle = 1.382 nJ
  6. 6. n = 1.513

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