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
f|I|0.70711 kHzf1​f2​BW = 20 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 20 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 20 Hz
Q =
2.Easy
C = 10 nFL = 1 mH

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

L = 1 mHC = 10 nF
f0 = kHz
3.Medium
tvC​iL​T/4 = ?T/2TL = 47 mHC = 10 pF

In an ideal LC circuit with L = 47 mH and C = 10 pF, 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 = 47 mHC = 10 pF
t = µs
4.Medium
V10 kΩ2.2 mH470 pF

A parallel RLC circuit has R = 10 kΩ, L = 2.2 mH and C = 470 pF. Find its quality factor Q.

R = 10 kΩL = 2.2 mHC = 470 pF
Q =
5.Hard
C = 1 nFR = 20 ΩL = 47 mH

A charged 1 nF capacitor discharges through a 47 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 = 47 mHC = 1 nFR = 20 Ω
n =
6.Hard
VR = ?100 µHC

A series resonant circuit uses a 100 µH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 100 µHBW = 100 kHz
R = Ω

Answer key

  1. 1. Q = 50
  2. 2. f0 = 50.33 kHz
  3. 3. t = 1.077 µs
  4. 4. Q = 4.622
  5. 5. n = 75.63
  6. 6. R = 62.83 Ω

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