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
tvC​iL​T/4T/2TV0​ = 9 VC = 2.2 µF

A 2.2 µF capacitor is charged to 9 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in µJ.

C = 2.2 µFV0 = 9 VL = 1 mH
W = µJ
2.Easy
f|I|0.70715 kHzf1​f2​BW = ?

A tuned circuit resonates at 5 kHz and has a quality factor Q = 40. Find its bandwidth BW in Hz.

f0 = 5 kHzQ = 40
BW = Hz
3.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 2.5
f1 = kHz
4.Medium
C = 2.2 µF+−5 VL = 1 µHiL​

A 2.2 µF capacitor charged to 20 V oscillates with an ideal 1 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 5 V, in µJ.

C = 2.2 µFV0 = 20 VvC = 5 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?5 kHz6 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 6 kHz
Q =
6.Hard
f|I|0.7071f0​ = ?100 kHz110 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 110 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 110 kHz
Q =

Answer key

  1. 1. W = 89.1 µJ
  2. 2. BW = 125 Hz
  3. 3. f1 = 1.64 kHz
  4. 4. WL = 412.5 µJ
  5. 5. Q = 5.477
  6. 6. Q = 10.49

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