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 = 22 nFL = 1 mH

An ideal LC circuit has L = 1 mH and C = 22 nF. Find its natural (resonance) frequency f0 in kHz.

L = 1 mHC = 22 nF
f0 = kHz
2.Easy
f|I|0.70711 kHzf1​f2​BW = 200 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 200 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 200 Hz
Q =
3.Medium
V10 Ω22 µH2.2 nF

A series RLC circuit has R = 10 Ω, L = 22 µH and C = 2.2 nF. Find its quality factor Q.

R = 10 ΩL = 22 µHC = 2.2 nF
Q =
4.Medium
C = 220 nF+−12 VL = 220 µHiL​

A 220 nF capacitor charged to 24 V oscillates with an ideal 220 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 12 V, in µJ.

C = 220 nFV0 = 24 VvC = 12 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?2 kHz2.4 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 2.4 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 2.4 kHz
Q =
6.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 455 kHz and a bandwidth of 11.38 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 455 kHzBW = 11.38 kHz
C = nF

Answer key

  1. 1. f0 = 33.93 kHz
  2. 2. Q = 5
  3. 3. Q = 10
  4. 4. WL = 47.52 µJ
  5. 5. Q = 5.477
  6. 6. C = 0.1749 nF

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