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 = 22 mH

An ideal LC circuit has L = 22 mH and C = 1 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 1 nF
f0 = kHz
2.Easy
C = 100 nFL = 220 µH

An ideal LC circuit has L = 220 µH and C = 100 nF. Find its natural (resonance) frequency f0 in kHz.

L = 220 µHC = 100 nF
f0 = kHz
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 4
f1 = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 mHC = 10 nF

In an ideal LC circuit with L = 2.2 mH and C = 10 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 = 2.2 mHC = 10 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?20 kHz30 kHzBW

The half-power frequencies of a resonance curve are 20 kHz and 30 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 20 kHzf2 = 30 kHz
Q =
6.Hard
C = 100 nFR = 1 ΩL = 2.2 mH

A charged 100 nF capacitor discharges through a 2.2 mH coil with a total series resistance of 1 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 = 2.2 mHC = 100 nFR = 1 Ω
n =

Answer key

  1. 1. f0 = 33.93 kHz
  2. 2. f0 = 33.93 kHz
  3. 3. f1 = 882.8 Hz
  4. 4. t = 7.368 µs
  5. 5. Q = 2.449
  6. 6. n = 32.73

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