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
tvC​iL​T/4T/2TV0​ = 2 VC = 10 µF

A 10 µF capacitor is charged to 2 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 2 VL = 1 mH
W = µJ
2.Easy
C = ?L = 22 µH

An LC circuit with L = 22 µH must resonate at 50 kHz. Find the capacitance C in nF.

L = 22 µHf0 = 50 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 220 µHC = 470 pF

In an ideal LC circuit with L = 220 µH and C = 470 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 = 470 pF
t = µs
4.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 3
f1 = kHz
5.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 470 µHBW = 1 kHz
R = Ω
6.Hard
V10 Ω4.7 mH220 nF10 mA

A series RLC circuit (R = 10 Ω, L = 4.7 mH, C = 220 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 = 4.7 mHC = 220 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. W = 20 µJ
  2. 2. C = 460.6 nF
  3. 3. t = 0.5051 µs
  4. 4. f1 = 8.471 kHz
  5. 5. R = 2.953 Ω
  6. 6. Ecycle = 101 nJ

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