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 = 2.2 µFL = 100 µH

An ideal LC circuit has L = 100 µH and C = 2.2 µF. Find its natural (resonance) frequency f0 in kHz.

L = 100 µHC = 2.2 µF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 9 VC = 10 µF

A 10 µF capacitor is charged to 9 V and then connected to an ideal 10 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 9 VL = 10 µH
W = µJ
3.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 5
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 220 µHC = 220 pF

In an ideal LC circuit with L = 220 µH 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 = 220 µHC = 220 pF
t = µs
5.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 455 kHz and a bandwidth of 45.5 kHz. Find the capacitance C in nF.

R = 10 Ωf0 = 455 kHzBW = 45.5 kHz
C = nF
6.Hard
C = 47 nFr = 2 ΩL = 470 µH

A parallel tank circuit is made of a 47 nF capacitor and a 470 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 470 µHC = 47 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. f0 = 10.73 kHz
  2. 2. W = 405 µJ
  3. 3. f1 = 9.05 kHz
  4. 4. t = 0.3456 µs
  5. 5. C = 3.498 nF
  6. 6. RD = 5 kΩ

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