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​ = 50 VC = 100 nF

A 100 nF capacitor is charged to 50 V and then connected to an ideal 470 µH inductor. Find the total energy W that swings between them, in µJ.

C = 100 nFV0 = 50 VL = 470 µH
W = µJ
2.Easy
tvC​iL​T/4T/2TV0​ = 20 VC = 47 pF

A 47 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 = 47 pFV0 = 20 VL = 100 mH
W = nJ
3.Medium
V47 Ω1 mH100 nF

A series RLC circuit has R = 47 Ω, L = 1 mH and C = 100 nF. Find its quality factor Q.

R = 47 ΩL = 1 mHC = 100 nF
Q =
4.Medium
V100 kΩ1 mH4.7 nF

A parallel RLC circuit has R = 100 kΩ, L = 1 mH and C = 4.7 nF. Find its quality factor Q.

R = 100 kΩL = 1 mHC = 4.7 nF
Q =
5.Hard
C = 2.2 nFR = 20 ΩL = 2.2 mH

A charged 2.2 nF capacitor discharges through a 2.2 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 = 2.2 mHC = 2.2 nFR = 20 Ω
n =
6.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 22 µHBW = 10 kHz
R = Ω

Answer key

  1. 1. W = 125 µJ
  2. 2. W = 9.4 nJ
  3. 3. Q = 2.128
  4. 4. Q = 216.8
  5. 5. n = 11.03
  6. 6. R = 1.382 Ω

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