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 = 47 nF+−10 VL = 2.2 mHiL​

A 47 nF capacitor charged to 10 V is switched across an ideal 2.2 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 10 VL = 2.2 mH
Imax = mA
2.Easy
tvC​iL​T/4T/2TV0​ = 12 VC = 22 nF

A 22 nF capacitor is charged to 12 V and then connected to an ideal 22 µH inductor. Find the total energy W that swings between them, in µJ.

C = 22 nFV0 = 12 VL = 22 µH
W = µJ
3.Medium
V2.2 kΩ100 µH2.2 nF

A parallel RLC circuit has R = 2.2 kΩ, L = 100 µH and C = 2.2 nF. Find its quality factor Q.

R = 2.2 kΩL = 100 µHC = 2.2 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 220 µHC = 470 nF

In an ideal LC circuit with L = 220 µH and C = 470 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 = 220 µHC = 470 nF
t = µs
5.Hard
V5 Ω220 µH470 nF10 mA

A series RLC circuit (R = 5 Ω, L = 220 µH, C = 470 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 = 5 ΩL = 220 µHC = 470 nFIm = 10 mA
Ecycle = nJ
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 1 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 10 kHzBW = 1 kHz
C = nF

Answer key

  1. 1. Imax = 46.22 mA
  2. 2. W = 1.584 µJ
  3. 3. Q = 10.32
  4. 4. t = 15.97 µs
  5. 5. Ecycle = 15.97 nJ
  6. 6. C = 79.58 nF

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