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
tvC​iL​T/4T/2TV0​ = 20 VC = 10 pF

A 10 pF capacitor is charged to 20 V and then connected to an ideal 100 mH inductor. Find the total energy W that swings between them, in nJ.

C = 10 pFV0 = 20 VL = 100 mH
W = nJ
2.Easy
f|I|0.70711 MHzf1​f2​BW = ?

A tuned circuit resonates at 1 MHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 1 MHzQ = 8
BW = kHz
3.Medium
C = 1 µF+−3 VL = 0.47 µHiL​

A 1 µF capacitor charged to 15 V oscillates with an ideal 0.47 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3 V, in µJ.

C = 1 µFV0 = 15 VvC = 3 V
WL = µJ
4.Medium
V220 Ω1 mH1 nF

A series RLC circuit has R = 220 Ω, L = 1 mH and C = 1 nF. Find its bandwidth BW in kHz.

R = 220 ΩL = 1 mHC = 1 nF
BW = kHz
5.Hard
C = 22 nFR = 5 ΩL = 22 µH

A charged 22 nF capacitor discharges through a 22 µH 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 = 22 µHC = 22 nFR = 5 Ω
n =
6.Hard
f|I|0.7071f0​ = ?50 kHz100 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 100 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 100 kHz
Q =

Answer key

  1. 1. W = 2 nJ
  2. 2. BW = 125 kHz
  3. 3. WL = 108 µJ
  4. 4. BW = 35.01 kHz
  5. 5. n = 1.395
  6. 6. Q = 1.414

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