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
C = 470 pFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 470 pF. Find its natural (resonance) frequency f0 in MHz.

L = 47 µHC = 470 pF
f0 = MHz
2.Easy
C = 1 µFL = 100 µH

An ideal LC circuit has L = 100 µH and C = 1 µF. Find its natural (resonance) frequency f0 in kHz.

L = 100 µHC = 1 µF
f0 = kHz
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 3
f1 = kHz
4.Medium
C = 100 pF+−8 VL = 4.7 mHiL​

A 100 pF capacitor charged to 10 V oscillates with an ideal 4.7 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 8 V, in nJ.

C = 100 pFV0 = 10 VvC = 8 V
WL = nJ
5.Hard
C = 100 nFR = 20 ΩL = 22 mH

A charged 100 nF capacitor discharges through a 22 mH coil with a total series resistance of 20 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 mHC = 100 nFR = 20 Ω
n =
6.Hard
VR = ?10 µHC

A series resonant circuit uses a 10 µH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 10 µHBW = 10 kHz
R = Ω

Answer key

  1. 1. f0 = 1.071 MHz
  2. 2. f0 = 15.92 kHz
  3. 3. f1 = 423.6 kHz
  4. 4. WL = 1.8 nJ
  5. 5. n = 5.174
  6. 6. R = 0.6283 Ω

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