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​ = 3 VC = 470 nF

A 470 nF capacitor is charged to 3 V and then connected to an ideal 22 µH inductor. Find the total energy W that swings between them, in µJ.

C = 470 nFV0 = 3 VL = 22 µH
W = µJ
2.Easy
C = 100 nFL = 2.2 µH

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

L = 2.2 µHC = 100 nF
f0 = kHz
3.Medium
V1 Ω10 µH10 nF

A series RLC circuit has R = 1 Ω, L = 10 µH and C = 10 nF. Find its bandwidth BW in kHz.

R = 1 ΩL = 10 µHC = 10 nF
BW = kHz
4.Medium
V10 Ω22 mH10 nF

A series RLC circuit has R = 10 Ω, L = 22 mH and C = 10 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 22 mHC = 10 nF
BW = Hz
5.Hard
V5 Ω470 µH470 pF200 mA

A series RLC circuit (R = 5 Ω, L = 470 µH, C = 470 pF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 470 µHC = 470 pFIm = 200 mA
Ecycle = nJ
6.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 200 kHz and a bandwidth of 10 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 200 kHzBW = 10 kHz
C = nF

Answer key

  1. 1. W = 2.115 µJ
  2. 2. f0 = 339.3 kHz
  3. 3. BW = 15.92 kHz
  4. 4. BW = 72.34 Hz
  5. 5. Ecycle = 295.3 nJ
  6. 6. C = 0.7958 nF

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