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 nFL = 10 mH

An ideal LC circuit has L = 10 mH and C = 470 nF. Find its natural (resonance) frequency f0 in kHz.

L = 10 mHC = 470 nF
f0 = kHz
2.Easy
C = 47 pFL = 22 mH

An ideal LC circuit has L = 22 mH and C = 47 pF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 47 pF
f0 = kHz
3.Medium
V4.7 kΩ47 mH10 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 47 mH and C = 10 nF. Find its quality factor Q.

R = 4.7 kΩL = 47 mHC = 10 nF
Q =
4.Medium
V22 kΩ100 mH47 nF

A parallel RLC circuit has R = 22 kΩ, L = 100 mH and C = 47 nF. Find its quality factor Q.

R = 22 kΩL = 100 mHC = 47 nF
Q =
5.Hard
C = 220 nFR = 5 ΩL = 100 mH

A charged 220 nF capacitor discharges through a 100 mH coil with a total series resistance of 5 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 = 100 mHC = 220 nFR = 5 Ω
n =
6.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 470 µHBW = 2 kHz
R = Ω

Answer key

  1. 1. f0 = 2.322 kHz
  2. 2. f0 = 156.5 kHz
  3. 3. Q = 2.168
  4. 4. Q = 15.08
  5. 5. n = 29.75
  6. 6. R = 5.906 Ω

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