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​ = 9 VC = 10 µF

A 10 µF capacitor is charged to 9 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 9 VL = 220 µH
W = µJ
2.Easy
f|I|0.70711 kHzf1​f2​BW = 20 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 20 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 20 Hz
Q =
3.Medium
tvC​iL​T/4 = ?T/2TL = 100 µHC = 4.7 nF

In an ideal LC circuit with L = 100 µH and C = 4.7 nF, 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 = 100 µHC = 4.7 nF
t = µs
4.Medium
tvC​iL​T/4 = ?T/2TL = 100 mHC = 10 nF

In an ideal LC circuit with L = 100 mH and C = 10 nF, 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 = 100 mHC = 10 nF
t = µs
5.Hard
VR = ?100 µHC

A series resonant circuit uses a 100 µH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 100 µHBW = 2 kHz
R = Ω
6.Hard
V2 Ω10 µH220 nF10 mA

A series RLC circuit (R = 2 Ω, L = 10 µH, C = 220 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 10 µHC = 220 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. W = 405 µJ
  2. 2. Q = 50
  3. 3. t = 1.077 µs
  4. 4. t = 49.67 µs
  5. 5. R = 1.257 Ω
  6. 6. Ecycle = 0.9319 nJ

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