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 = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 5 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 5 kHz
C = nF
2.Easy
f|I|0.7071500 kHzf1​f2​BW = 12.5 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 12.5 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 12.5 kHz
Q =
3.Medium
C = 47 pF+−6 VL = 2.2 mHiL​

A 47 pF capacitor charged to 10 V oscillates with an ideal 2.2 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in nJ.

C = 47 pFV0 = 10 VvC = 6 V
WL = nJ
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 100 nF

In an ideal LC circuit with L = 1 mH 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 = 1 mHC = 100 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?8 kHz9.6 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 9.6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 9.6 kHz
Q =
6.Hard
C = 22 nFR = 20 ΩL = 1 mH

A charged 22 nF capacitor discharges through a 1 mH coil with a total series resistance of 20 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 = 1 mHC = 22 nFR = 20 Ω
n =

Answer key

  1. 1. C = 215.6 nF
  2. 2. Q = 40
  3. 3. WL = 1.504 nJ
  4. 4. t = 15.71 µs
  5. 5. Q = 5.477
  6. 6. n = 2.352

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