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 = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 500 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 500 kHz
C = nF
2.Easy
C = ?L = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 10 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 10 kHz
C = nF
3.Medium
V22 Ω1 mH220 nF

A series RLC circuit has R = 22 Ω, L = 1 mH and C = 220 nF. Find its quality factor Q.

R = 22 ΩL = 1 mHC = 220 nF
Q =
4.Medium
C = 47 nF+−14.4 VL = 1 µHiL​

A 47 nF capacitor charged to 24 V oscillates with an ideal 1 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 14.4 V, in µJ.

C = 47 nFV0 = 24 VvC = 14.4 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?10 kHz25 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 25 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 25 kHz
Q =
6.Hard
f|I|0.7071f0​ = ?100 kHz120 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 120 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 120 kHz
Q =

Answer key

  1. 1. C = 0.1013 nF
  2. 2. C = 53.89 nF
  3. 3. Q = 3.065
  4. 4. WL = 8.663 µJ
  5. 5. Q = 1.054
  6. 6. Q = 5.477

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