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 = 22 nF+−3 VL = 22 mHiL​

A 22 nF capacitor charged to 3 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 22 nFV0 = 3 VL = 22 mH
Imax = mA
2.Easy
tvC​iL​T/4T/2TV0​ = 20 VC = 1 nF

A 1 nF capacitor is charged to 20 V and then connected to an ideal 470 µH inductor. Find the total energy W that swings between them, in nJ.

C = 1 nFV0 = 20 VL = 470 µH
W = nJ
3.Medium
V5 Ω47 µH10 nF

A series RLC circuit has R = 5 Ω, L = 47 µH and C = 10 nF. Find its quality factor Q.

R = 5 ΩL = 47 µHC = 10 nF
Q =
4.Medium
C = 220 nF+−1.5 VL = 100 µHiL​

A 220 nF capacitor charged to 6 V oscillates with an ideal 100 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.5 V, in µJ.

C = 220 nFV0 = 6 VvC = 1.5 V
WL = µJ
5.Hard
C = 47 nFR = 1 ΩL = 4.7 mH

A charged 47 nF capacitor discharges through a 4.7 mH 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 = 4.7 mHC = 47 nFR = 1 Ω
n =
6.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 50 kHzBW = 2 kHz
C = nF

Answer key

  1. 1. Imax = 3 mA
  2. 2. W = 200 nJ
  3. 3. Q = 13.71
  4. 4. WL = 3.712 µJ
  5. 5. n = 69.77
  6. 6. C = 1.273 nF

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