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|0.70712 kHzf1​f2​BW = ?

A tuned circuit resonates at 2 kHz and has a quality factor Q = 80. Find its bandwidth BW in Hz.

f0 = 2 kHzQ = 80
BW = Hz
2.Easy
f|I|0.70712 kHzf1​f2​BW = ?

A tuned circuit resonates at 2 kHz and has a quality factor Q = 8. Find its bandwidth BW in Hz.

f0 = 2 kHzQ = 8
BW = Hz
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 3
f1 = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 µHC = 1 µF

In an ideal LC circuit with L = 22 µH and C = 1 µF, 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 = 22 µHC = 1 µF
t = µs
5.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 100 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 10 Ωf0 = 100 kHzBW = 5 kHz
C = nF
6.Hard
C = 2.2 nFR = 20 ΩL = 47 µH

A charged 2.2 nF capacitor discharges through a 47 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 = 47 µHC = 2.2 nFR = 20 Ω
n =

Answer key

  1. 1. BW = 25 Hz
  2. 2. BW = 250 Hz
  3. 3. f1 = 847.1 Hz
  4. 4. t = 7.368 µs
  5. 5. C = 7.958 nF
  6. 6. n = 1.612

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