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 = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 200 kHz
C = nF
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = ?

A tuned circuit resonates at 1.6 MHz and has a quality factor Q = 10. Find its bandwidth BW in kHz.

f0 = 1.6 MHzQ = 10
BW = kHz
3.Medium
V2 Ω4.7 mH220 nF

A series RLC circuit has R = 2 Ω, L = 4.7 mH and C = 220 nF. Find its bandwidth BW in Hz.

R = 2 ΩL = 4.7 mHC = 220 nF
BW = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 470 nF

In an ideal LC circuit with L = 1 mH and C = 470 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 = 1 mHC = 470 nF
t = µs
5.Hard
V10 Ω470 µH10 nF10 mA

A series RLC circuit (R = 10 Ω, L = 470 µH, C = 10 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 = 10 ΩL = 470 µHC = 10 nFIm = 10 mA
Ecycle = nJ
6.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 10 Ωf0 = 50 kHzBW = 2 kHz
C = nF

Answer key

  1. 1. C = 0.6333 nF
  2. 2. BW = 160 kHz
  3. 3. BW = 67.73 Hz
  4. 4. t = 34.05 µs
  5. 5. Ecycle = 6.811 nJ
  6. 6. C = 12.73 nF

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