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|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 20
BW = kHz
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = ?

A tuned circuit resonates at 1.6 MHz and has a quality factor Q = 12. Find its bandwidth BW in kHz.

f0 = 1.6 MHzQ = 12
BW = kHz
3.Medium
V22 Ω2.2 mH47 nF

A series RLC circuit has R = 22 Ω, L = 2.2 mH and C = 47 nF. Find its bandwidth BW in kHz.

R = 22 ΩL = 2.2 mHC = 47 nF
BW = kHz
4.Medium
C = 47 pF+−7.5 VL = 22 mHiL​

A 47 pF capacitor charged to 10 V oscillates with an ideal 22 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 7.5 V, in nJ.

C = 47 pFV0 = 10 VvC = 7.5 V
WL = nJ
5.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 500 kHz and a bandwidth of 25 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 500 kHzBW = 25 kHz
C = nF
6.Hard
C = 100 nFR = 1 ΩL = 10 µH

A charged 100 nF capacitor discharges through a 10 µH coil with a total series resistance of 1 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 µHC = 100 nFR = 1 Ω
n =

Answer key

  1. 1. BW = 535 kHz
  2. 2. BW = 133.3 kHz
  3. 3. BW = 1.592 kHz
  4. 4. WL = 1.028 nJ
  5. 5. C = 0.1592 nF
  6. 6. n = 2.206

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