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 = 83.33 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 83.33 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 83.33 Hz
Q =
2.Easy
tvC​iL​T/4T/2TV0​ = 9 VC = 1 nF

A 1 nF capacitor is charged to 9 V and then connected to an ideal 47 µH inductor. Find the total energy W that swings between them, in nJ.

C = 1 nFV0 = 9 VL = 47 µH
W = nJ
3.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 220 nF

In an ideal LC circuit with L = 1 mH and C = 220 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 = 220 nF
t = µs
4.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 2.5
f1 = kHz
5.Hard
C = 470 pFR = 20 ΩL = 100 µH

A charged 470 pF capacitor discharges through a 100 µH 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 = 100 µHC = 470 pFR = 20 Ω
n =
6.Hard
C = 2.2 µFR = 5 ΩL = 10 mH

A charged 2.2 µF capacitor discharges through a 10 mH coil with a total series resistance of 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 = 10 mHC = 2.2 µFR = 5 Ω
n =

Answer key

  1. 1. Q = 12
  2. 2. W = 40.5 nJ
  3. 3. t = 23.3 µs
  4. 4. f1 = 1.64 kHz
  5. 5. n = 5.089
  6. 6. n = 2.975

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