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|0.7071500 kHzf1​f2​BW = ?

A tuned circuit resonates at 500 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 500 kHzQ = 8
BW = kHz
2.Easy
f|I|0.707150 kHzf1​f2​BW = 5 kHz

A resonance curve peaks at 50 kHz, and its half-power points are 5 kHz apart. Find the quality factor Q.

f0 = 50 kHzBW = 5 kHz
Q =
3.Medium
C = 2.2 µF+−3 VL = 2.2 mHiL​

A 2.2 µF capacitor charged to 5 V oscillates with an ideal 2.2 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3 V, in µJ.

C = 2.2 µFV0 = 5 VvC = 3 V
WL = µJ
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 2.2 nF

In an ideal LC circuit with L = 1 mH and C = 2.2 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 1 mHC = 2.2 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?8 kHz16 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 16 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 16 kHz
Q =
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 100 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 100 kHzBW = 4 kHz
C = nF

Answer key

  1. 1. BW = 62.5 kHz
  2. 2. Q = 10
  3. 3. WL = 17.6 µJ
  4. 4. t = 2.33 µs
  5. 5. Q = 1.414
  6. 6. C = 12.73 nF

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