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 = 220 pFL = 100 µH

An ideal LC circuit has L = 100 µH and C = 220 pF. Find its natural (resonance) frequency f0 in MHz.

L = 100 µHC = 220 pF
f0 = MHz
2.Easy
C = 10 nFL = 100 mH

An ideal LC circuit has L = 100 mH and C = 10 nF. Find its natural (resonance) frequency f0 in kHz.

L = 100 mHC = 10 nF
f0 = kHz
3.Medium
C = 470 pF+−6 VL = 2.2 mHiL​

A 470 pF capacitor charged to 24 V oscillates with an ideal 2.2 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in nJ.

C = 470 pFV0 = 24 VvC = 6 V
WL = nJ
4.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2.5
f1 = kHz
5.Hard
VR = ?22 mHC

A series resonant circuit uses a 22 mH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 22 mHBW = 500 Hz
R = Ω
6.Hard
C = 4.7 nFr = 20 ΩL = 22 mH

A parallel tank circuit is made of a 4.7 nF capacitor and a 22 mH coil with a winding resistance of 20 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 22 mHC = 4.7 nFr = 20 Ω
RD = kΩ

Answer key

  1. 1. f0 = 1.073 MHz
  2. 2. f0 = 5.033 kHz
  3. 3. WL = 126.9 nJ
  4. 4. f1 = 4.099 kHz
  5. 5. R = 69.12 Ω
  6. 6. RD = 234 kΩ

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