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 nFL = 10 µH

An ideal LC circuit has L = 10 µH and C = 1 nF. Find its natural (resonance) frequency f0 in MHz.

L = 10 µHC = 1 nF
f0 = MHz
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 2 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 2 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 470 µHC = 100 nF

In an ideal LC circuit with L = 470 µH and C = 100 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 = 470 µHC = 100 nF
t = µs
4.Medium
V22 Ω2.2 mH470 pF

A series RLC circuit has R = 22 Ω, L = 2.2 mH and C = 470 pF. Find its quality factor Q.

R = 22 ΩL = 2.2 mHC = 470 pF
Q =
5.Hard
C = 10 nFR = 0.5 ΩL = 47 µH

A charged 10 nF capacitor discharges through a 47 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 = 47 µHC = 10 nFR = 0.5 Ω
n =
6.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 500 kHz and a bandwidth of 12.5 kHz. Find the capacitance C in nF.

R = 10 Ωf0 = 500 kHzBW = 12.5 kHz
C = nF

Answer key

  1. 1. f0 = 1.592 MHz
  2. 2. C = 2878 nF
  3. 3. t = 10.77 µs
  4. 4. Q = 98.34
  5. 5. n = 30.25
  6. 6. C = 0.7958 nF

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