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|0.70715 kHzf1​f2​BW = ?

A tuned circuit resonates at 5 kHz and has a quality factor Q = 40. Find its bandwidth BW in Hz.

f0 = 5 kHzQ = 40
BW = Hz
2.Easy
f|I|0.707150 kHzf1​f2​BW = ?

A tuned circuit resonates at 50 kHz and has a quality factor Q = 12. Find its bandwidth BW in kHz.

f0 = 50 kHzQ = 12
BW = kHz
3.Medium
tvC​iL​T/4 = ?T/2TL = 10 mHC = 220 pF

In an ideal LC circuit with L = 10 mH and C = 220 pF, 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 = 10 mHC = 220 pF
t = µs
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 µHC = 10 µF

In an ideal LC circuit with L = 2.2 µH and C = 10 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 = 2.2 µHC = 10 µF
t = µs
5.Hard
V5 Ω47 mH470 nF50 mA

A series RLC circuit (R = 5 Ω, L = 47 mH, C = 470 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 5 ΩL = 47 mHC = 470 nFIm = 50 mA
Ecycle = µJ
6.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 22 µHBW = 100 kHz
R = Ω

Answer key

  1. 1. BW = 125 Hz
  2. 2. BW = 4.167 kHz
  3. 3. t = 2.33 µs
  4. 4. t = 7.368 µs
  5. 5. Ecycle = 5.837 µJ
  6. 6. R = 13.82 Ω

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