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
f|I|0.707150 kHzf1​f2​BW = ?

A tuned circuit resonates at 50 kHz and has a quality factor Q = 40. Find its bandwidth BW in kHz.

f0 = 50 kHzQ = 40
BW = kHz
2.Easy
C = ?L = 22 mH

An LC circuit with L = 22 mH must resonate at 20 kHz. Find the capacitance C in nF.

L = 22 mHf0 = 20 kHz
C = nF
3.Medium
C = 220 nF+−6 VL = 10 mHiL​

A 220 nF capacitor charged to 15 V oscillates with an ideal 10 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in µJ.

C = 220 nFV0 = 15 VvC = 6 V
WL = µJ
4.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 2
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?400 kHz1 MHzBW

The half-power frequencies of a resonance curve are 400 kHz and 1 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 1 MHz
Q =
6.Hard
VR = ?10 µHC

A series resonant circuit uses a 10 µH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 10 µHBW = 20 kHz
R = Ω

Answer key

  1. 1. BW = 1.25 kHz
  2. 2. C = 2.878 nF
  3. 3. WL = 20.79 µJ
  4. 4. f1 = 390.4 kHz
  5. 5. Q = 1.054
  6. 6. R = 1.257 Ω

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