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​ = 9 VC = 10 nF

A 10 nF capacitor is charged to 9 V and then connected to an ideal 1 µH inductor. Find the total energy W that swings between them, in nJ.

C = 10 nFV0 = 9 VL = 1 µH
W = nJ
2.Easy
tvC​iL​T/4T/2TV0​ = 2 VC = 2.2 nF

A 2.2 nF capacitor is charged to 2 V and then connected to an ideal 47 µH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 2 VL = 47 µH
W = nJ
3.Medium
V22 kΩ100 mH10 nF

A parallel RLC circuit has R = 22 kΩ, L = 100 mH and C = 10 nF. Find its quality factor Q.

R = 22 kΩL = 100 mHC = 10 nF
Q =
4.Medium
V22 Ω47 µH10 nF

A series RLC circuit has R = 22 Ω, L = 47 µH and C = 10 nF. Find its quality factor Q.

R = 22 ΩL = 47 µHC = 10 nF
Q =
5.Hard
f|I|0.7071f0​ = ?8 kHz8.8 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 8.8 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 8.8 kHz
Q =
6.Hard
C = 4.7 nFR = 20 ΩL = 470 µH

A charged 4.7 nF capacitor discharges through a 470 µH 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 = 470 µHC = 4.7 nFR = 20 Ω
n =

Answer key

  1. 1. W = 405 nJ
  2. 2. W = 4.4 nJ
  3. 3. Q = 6.957
  4. 4. Q = 3.116
  5. 5. Q = 10.49
  6. 6. n = 3.489

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