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|0.7071100 kHzf1​f2​BW = 2.5 kHz

A resonance curve peaks at 100 kHz, and its half-power points are 2.5 kHz apart. Find the quality factor Q.

f0 = 100 kHzBW = 2.5 kHz
Q =
2.Easy
C = ?L = 220 µH

An LC circuit with L = 220 µH must resonate at 5 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 5 kHz
C = nF
3.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 4
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 mHC = 10 µF

In an ideal LC circuit with L = 2.2 mH 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 mHC = 10 µF
t = µs
5.Hard
VR = ?1 mHC

A series resonant circuit uses a 1 mH inductor. Which total series resistance R gives a bandwidth of 5 kHz?

L = 1 mHBW = 5 kHz
R = Ω
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 20 kHz and a bandwidth of 500 Hz. Find the capacitance C in nF.

R = 20 Ωf0 = 20 kHzBW = 500 Hz
C = nF

Answer key

  1. 1. Q = 40
  2. 2. C = 4606 nF
  3. 3. f1 = 17.66 kHz
  4. 4. t = 233 µs
  5. 5. R = 31.42 Ω
  6. 6. C = 9.947 nF

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