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 = ?L = 220 µH

An LC circuit with L = 220 µH must resonate at 100 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 100 kHz
C = nF
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
V2.2 kΩ100 µH220 nF

A parallel RLC circuit has R = 2.2 kΩ, L = 100 µH and C = 220 nF. Find its quality factor Q.

R = 2.2 kΩL = 100 µHC = 220 nF
Q =
4.Medium
V220 Ω1 mH1 nF

A series RLC circuit has R = 220 Ω, L = 1 mH and C = 1 nF. Find its bandwidth BW in kHz.

R = 220 ΩL = 1 mHC = 1 nF
BW = kHz
5.Hard
C = 4.7 nFR = 10 ΩL = 22 µH

A charged 4.7 nF capacitor discharges through a 22 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 = 22 µHC = 4.7 nFR = 10 Ω
n =
6.Hard
C = 1 µFR = 0.5 ΩL = 470 µH

A charged 1 µF capacitor discharges through a 470 µH coil with a total series resistance of 0.5 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 = 470 µHC = 1 µFR = 0.5 Ω
n =

Answer key

  1. 1. C = 11.51 nF
  2. 2. f0 = 156.5 kHz
  3. 3. Q = 103.2
  4. 4. BW = 35.01 kHz
  5. 5. n = 1.51
  6. 6. n = 9.567

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