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​ = 50 VC = 100 nF

A 100 nF capacitor is charged to 50 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in µJ.

C = 100 nFV0 = 50 VL = 1 mH
W = µJ
2.Easy
C = 47 pFL = 22 mH

An ideal LC circuit has L = 22 mH and C = 47 pF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 47 pF
f0 = kHz
3.Medium
C = 47 pF+−9.6 VL = 10 mHiL​

A 47 pF capacitor charged to 24 V oscillates with an ideal 10 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 9.6 V, in nJ.

C = 47 pFV0 = 24 VvC = 9.6 V
WL = nJ
4.Medium
f|I|0.707150 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 50 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 50 kHzQ = 3
f1 = kHz
5.Hard
VR = ?2.2 mHC

A series resonant circuit uses a 2.2 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 2.2 mHBW = 50 kHz
R = Ω
6.Hard
C = 220 pFr = 5 ΩL = 2.2 mH

A parallel tank circuit is made of a 220 pF capacitor and a 2.2 mH coil with a winding resistance of 5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 2.2 mHC = 220 pFr = 5 Ω
RD = kΩ

Answer key

  1. 1. W = 125 µJ
  2. 2. f0 = 156.5 kHz
  3. 3. WL = 11.37 nJ
  4. 4. f1 = 42.36 kHz
  5. 5. R = 691.2 Ω
  6. 6. RD = 2000 kΩ

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