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 = 2.2 nF

A 2.2 nF capacitor is charged to 3 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 3 VL = 47 mH
W = nJ
2.Easy
tvC​iL​T/4T/2TV0​ = 1 VC = 47 nF

A 47 nF capacitor is charged to 1 V and then connected to an ideal 2.2 µH inductor. Find the total energy W that swings between them, in nJ.

C = 47 nFV0 = 1 VL = 2.2 µH
W = nJ
3.Medium
V22 Ω470 µH47 nF

A series RLC circuit has R = 22 Ω, L = 470 µH and C = 47 nF. Find its quality factor Q.

R = 22 ΩL = 470 µHC = 47 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 10 nF

In an ideal LC circuit with L = 1 mH and C = 10 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 = 1 mHC = 10 nF
t = µs
5.Hard
V22 Ω47 mH100 nF20 mA

A series RLC circuit (R = 22 Ω, L = 47 mH, C = 100 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 47 mHC = 100 nFIm = 20 mA
Ecycle = µJ
6.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 20 kHz and a bandwidth of 400 Hz. Find the capacitance C in nF.

R = 100 Ωf0 = 20 kHzBW = 400 Hz
C = nF

Answer key

  1. 1. W = 9.9 nJ
  2. 2. W = 23.5 nJ
  3. 3. Q = 4.545
  4. 4. t = 4.967 µs
  5. 5. Ecycle = 1.895 µJ
  6. 6. C = 1.592 nF

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