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 = 100 pF+−10 VL = 10 mHiL​

A 100 pF capacitor charged to 10 V is switched across an ideal 10 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 pFV0 = 10 VL = 10 mH
Imax = mA
2.Easy
C = ?L = 47 mH

An LC circuit with L = 47 mH must resonate at 20 kHz. Find the capacitance C in nF.

L = 47 mHf0 = 20 kHz
C = nF
3.Medium
C = 100 nF+−4.5 VL = 22 µHiL​

A 100 nF capacitor charged to 6 V oscillates with an ideal 22 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4.5 V, in nJ.

C = 100 nFV0 = 6 VvC = 4.5 V
WL = nJ
4.Medium
C = 10 µF+−1.5 VL = 2.2 mHiL​

A 10 µF capacitor charged to 6 V oscillates with an ideal 2.2 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.5 V, in µJ.

C = 10 µFV0 = 6 VvC = 1.5 V
WL = µJ
5.Hard
C = 220 pFr = 2 ΩL = 470 µH

A parallel tank circuit is made of a 220 pF capacitor and a 470 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 470 µHC = 220 pFr = 2 Ω
RD = kΩ
6.Hard
VR = ?100 µHC

A series resonant circuit uses a 100 µH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 100 µHBW = 10 kHz
R = Ω

Answer key

  1. 1. Imax = 1 mA
  2. 2. C = 1.347 nF
  3. 3. WL = 787.5 nJ
  4. 4. WL = 168.7 µJ
  5. 5. RD = 1068 kΩ
  6. 6. R = 6.283 Ω

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