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 = 37.92 kHz

A resonance curve peaks at 455 kHz, and its half-power points are 37.92 kHz apart. Find the quality factor Q.

f0 = 455 kHzBW = 37.92 kHz
Q =
2.Easy
tvC​iL​T/4T/2TV0​ = 50 VC = 4.7 nF

A 4.7 nF capacitor is charged to 50 V and then connected to an ideal 2.2 µH inductor. Find the total energy W that swings between them, in µJ.

C = 4.7 nFV0 = 50 VL = 2.2 µH
W = µJ
3.Medium
tvC​iL​T/4 = ?T/2TL = 0.47 µHC = 1 µF

In an ideal LC circuit with L = 0.47 µH and C = 1 µF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 0.47 µHC = 1 µF
t = µs
4.Medium
C = 10 nF+−6 VL = 1 mHiL​

A 10 nF capacitor charged to 10 V oscillates with an ideal 1 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in nJ.

C = 10 nFV0 = 10 VvC = 6 V
WL = nJ
5.Hard
C = 1 µFR = 0.5 ΩL = 4.7 mH

A charged 1 µF capacitor discharges through a 4.7 mH coil with a total series resistance of 0.5 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 = 1 µFR = 0.5 Ω
n =
6.Hard
V2 Ω10 mH1 µF50 mA

A series RLC circuit (R = 2 Ω, L = 10 mH, C = 1 µF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 2 ΩL = 10 mHC = 1 µFIm = 50 mA
Ecycle = µJ

Answer key

  1. 1. Q = 12
  2. 2. W = 5.875 µJ
  3. 3. t = 1.077 µs
  4. 4. WL = 320 nJ
  5. 5. n = 30.25
  6. 6. Ecycle = 1.571 µJ

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