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|0.7071455 kHzf1​f2​BW = ?

A tuned circuit resonates at 455 kHz and has a quality factor Q = 80. Find its bandwidth BW in kHz.

f0 = 455 kHzQ = 80
BW = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 3 VC = 470 nF

A 470 nF capacitor is charged to 3 V and then connected to an ideal 10 mH inductor. Find the total energy W that swings between them, in µJ.

C = 470 nFV0 = 3 VL = 10 mH
W = µJ
3.Medium
V22 Ω2.2 mH4.7 nF

A series RLC circuit has R = 22 Ω, L = 2.2 mH and C = 4.7 nF. Find its quality factor Q.

R = 22 ΩL = 2.2 mHC = 4.7 nF
Q =
4.Medium
V220 Ω1 mH4.7 nF

A series RLC circuit has R = 220 Ω, L = 1 mH and C = 4.7 nF. Find its quality factor Q.

R = 220 ΩL = 1 mHC = 4.7 nF
Q =
5.Hard
C = 22 nFR = 2 ΩL = 10 mH

A charged 22 nF capacitor discharges through a 10 mH coil with a total series resistance of 2 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 mHC = 22 nFR = 2 Ω
n =
6.Hard
VR = ?47 µHC

A series resonant circuit uses a 47 µH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 47 µHBW = 50 kHz
R = Ω

Answer key

  1. 1. BW = 5.688 kHz
  2. 2. W = 2.115 µJ
  3. 3. Q = 31.1
  4. 4. Q = 2.097
  5. 5. n = 74.38
  6. 6. R = 14.77 Ω

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