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​ = 6 VC = 2.2 nF

A 2.2 nF capacitor is charged to 6 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 6 VL = 4.7 mH
W = nJ
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 50. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 50
BW = kHz
3.Medium
V4.7 kΩ4.7 mH2.2 nF

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

R = 4.7 kΩL = 4.7 mHC = 2.2 nF
Q =
4.Medium
V220 Ω4.7 mH1 nF

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

R = 220 ΩL = 4.7 mHC = 1 nF
Q =
5.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 200 kHz and a bandwidth of 10 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 200 kHzBW = 10 kHz
C = nF
6.Hard
C = 47 nFR = 1 ΩL = 2.2 µH

A charged 47 nF capacitor discharges through a 2.2 µH coil with a total series resistance of 1 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 µHC = 47 nFR = 1 Ω
n =

Answer key

  1. 1. W = 39.6 nJ
  2. 2. BW = 214 kHz
  3. 3. Q = 3.216
  4. 4. Q = 9.854
  5. 5. C = 7.958 nF
  6. 6. n = 1.51

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