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 mH

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

L = 47 mHC = 470 pF
f0 = kHz
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 200 kHz
C = nF
3.Medium
V1 kΩ470 µH1 µF

A parallel RLC circuit has R = 1 kΩ, L = 470 µH and C = 1 µF. Find its quality factor Q.

R = 1 kΩL = 470 µHC = 1 µF
Q =
4.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
5.Hard
C = 2.2 nFR = 20 ΩL = 100 mH

A charged 2.2 nF capacitor discharges through a 100 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 = 100 mHC = 2.2 nFR = 20 Ω
n =
6.Hard
C = 47 nFR = 0.5 ΩL = 1 µH

A charged 47 nF capacitor discharges through a 1 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 = 1 µHC = 47 nFR = 0.5 Ω
n =

Answer key

  1. 1. f0 = 33.86 kHz
  2. 2. C = 0.2878 nF
  3. 3. Q = 46.13
  4. 4. f1 = 423.6 kHz
  5. 5. n = 74.38
  6. 6. n = 2.035

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