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​ = 6 VC = 2.2 nF

A 2.2 nF capacitor is charged to 6 V and then connected to an ideal 100 µH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 6 VL = 100 µH
W = nJ
2.Easy
tvC​iL​T/4T/2TV0​ = 50 VC = 10 nF

A 10 nF capacitor is charged to 50 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in µJ.

C = 10 nFV0 = 50 VL = 4.7 mH
W = µJ
3.Medium
C = 470 nF+−1.2 VL = 1 mHiL​

A 470 nF capacitor charged to 6 V oscillates with an ideal 1 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.2 V, in µJ.

C = 470 nFV0 = 6 VvC = 1.2 V
WL = µJ
4.Medium
V22 kΩ470 µH100 pF

A parallel RLC circuit has R = 22 kΩ, L = 470 µH and C = 100 pF. Find its quality factor Q.

R = 22 kΩL = 470 µHC = 100 pF
Q =
5.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 100 mHBW = 50 kHz
R = Ω
6.Hard
V2 Ω100 µH47 nF20 mA

A series RLC circuit (R = 2 Ω, L = 100 µH, C = 47 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 100 µHC = 47 nFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. W = 39.6 nJ
  2. 2. W = 12.5 µJ
  3. 3. WL = 8.122 µJ
  4. 4. Q = 10.15
  5. 5. R = 31416 Ω
  6. 6. Ecycle = 5.449 nJ

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