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 = 470 pFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 470 pF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 470 pF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 24 VC = 10 pF

A 10 pF capacitor is charged to 24 V and then connected to an ideal 10 mH inductor. Find the total energy W that swings between them, in nJ.

C = 10 pFV0 = 24 VL = 10 mH
W = nJ
3.Medium
V220 Ω2.2 mH220 pF

A series RLC circuit has R = 220 Ω, L = 2.2 mH and C = 220 pF. Find its quality factor Q.

R = 220 ΩL = 2.2 mHC = 220 pF
Q =
4.Medium
V10 Ω10 mH220 nF

A series RLC circuit has R = 10 Ω, L = 10 mH and C = 220 nF. Find its quality factor Q.

R = 10 ΩL = 10 mHC = 220 nF
Q =
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
VR = ?220 µHC

A series resonant circuit uses a 220 µH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 220 µHBW = 2 kHz
R = Ω

Answer key

  1. 1. f0 = 338.6 kHz
  2. 2. W = 2.88 nJ
  3. 3. Q = 14.37
  4. 4. Q = 21.32
  5. 5. Q = 5.477
  6. 6. R = 2.765 Ω

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