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 mH

An LC circuit with L = 2.2 mH must resonate at 50 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 50 kHz
C = nF
2.Easy
f|I|0.7071500 kHzf1​f2​BW = ?

A tuned circuit resonates at 500 kHz and has a quality factor Q = 12. Find its bandwidth BW in kHz.

f0 = 500 kHzQ = 12
BW = kHz
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 1.5
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 mHC = 100 pF

In an ideal LC circuit with L = 22 mH and C = 100 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 = 22 mHC = 100 pF
t = µs
5.Hard
V22 Ω470 µH100 nF200 mA

A series RLC circuit (R = 22 Ω, L = 470 µH, C = 100 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 470 µHC = 100 nFIm = 200 mA
Ecycle = µJ
6.Hard
VR = ?47 µHC

A series resonant circuit uses a 47 µH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 47 µHBW = 100 kHz
R = Ω

Answer key

  1. 1. C = 4.606 nF
  2. 2. BW = 41.67 kHz
  3. 3. f1 = 360.4 kHz
  4. 4. t = 2.33 µs
  5. 5. Ecycle = 18.95 µJ
  6. 6. R = 29.53 Ω

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