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|0.707110 kHzf1​f2​BW = 100 Hz

A resonance curve peaks at 10 kHz, and its half-power points are 100 Hz apart. Find the quality factor Q.

f0 = 10 kHzBW = 100 Hz
Q =
2.Easy
f|I|0.7071455 kHzf1​f2​BW = ?

A tuned circuit resonates at 455 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 455 kHzQ = 8
BW = kHz
3.Medium
C = 470 pF+−1.25 VL = 100 µHiL​

A 470 pF capacitor charged to 5 V oscillates with an ideal 100 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.25 V, in nJ.

C = 470 pFV0 = 5 VvC = 1.25 V
WL = nJ
4.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 3
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?5 kHz8 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 8 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 8 kHz
Q =
6.Hard
C = 100 nFR = 5 ΩL = 10 mH

A charged 100 nF 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 = 100 nFR = 5 Ω
n =

Answer key

  1. 1. Q = 100
  2. 2. BW = 56.88 kHz
  3. 3. WL = 5.508 nJ
  4. 4. f1 = 84.71 kHz
  5. 5. Q = 2.108
  6. 6. n = 13.95

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