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 = 2.2 µH

An LC circuit with L = 2.2 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 2.2 µHf0 = 1 MHz
C = nF
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 455 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 455 kHz
C = nF
3.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 4
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 100 mHC = 1 nF

In an ideal LC circuit with L = 100 mH and C = 1 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 = 1 nF
t = µs
5.Hard
VR = ?10 mHC

A series resonant circuit uses a 10 mH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 10 mHBW = 100 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?100 kHz110 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 110 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 110 kHz
Q =

Answer key

  1. 1. C = 11.51 nF
  2. 2. C = 0.05562 nF
  3. 3. f1 = 8.828 kHz
  4. 4. t = 15.71 µs
  5. 5. R = 6283 Ω
  6. 6. Q = 10.49

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