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 = 20. Find its bandwidth BW in Hz.

f0 = 2 kHzQ = 20
BW = Hz
2.Easy
C = ?L = 220 µH

An LC circuit with L = 220 µH must resonate at 500 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 500 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 100 mHC = 47 nF

In an ideal LC circuit with L = 100 mH and C = 47 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 = 100 mHC = 47 nF
t = µs
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 mHC = 1 nF

In an ideal LC circuit with L = 2.2 mH and C = 1 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 = 1 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?10 kHz10.5 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 10.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 10.5 kHz
Q =
6.Hard
C = 100 nFR = 2 ΩL = 1 mH

A charged 100 nF capacitor discharges through a 1 mH coil with a total series resistance of 2 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 = 100 nFR = 2 Ω
n =

Answer key

  1. 1. BW = 100 Hz
  2. 2. C = 0.4606 nF
  3. 3. t = 107.7 µs
  4. 4. t = 2.33 µs
  5. 5. Q = 20.49
  6. 6. n = 11.03

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