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|0.7071500 kHzf1​f2​BW = 10 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 10 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 10 kHz
Q =
2.Easy
tvC​iL​T/4T/2TV0​ = 3 VC = 22 nF

A 22 nF capacitor is charged to 3 V and then connected to an ideal 10 µH inductor. Find the total energy W that swings between them, in nJ.

C = 22 nFV0 = 3 VL = 10 µH
W = nJ
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2.5
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 0.47 µHC = 1 µF

In an ideal LC circuit with L = 0.47 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 = 0.47 µHC = 1 µF
t = µs
5.Hard
C = 47 nFR = 0.5 ΩL = 47 µH

A charged 47 nF capacitor discharges through a 47 µH coil with a total series resistance of 0.5 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 = 47 µHC = 47 nFR = 0.5 Ω
n =
6.Hard
f|I|0.7071f0​ = ?50 kHz55 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 55 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 55 kHz
Q =

Answer key

  1. 1. Q = 50
  2. 2. W = 99 nJ
  3. 3. f1 = 4.099 kHz
  4. 4. t = 1.077 µs
  5. 5. n = 13.95
  6. 6. Q = 10.49

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