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 = 100 pFL = 47 mH

An ideal LC circuit has L = 47 mH and C = 100 pF. Find its natural (resonance) frequency f0 in kHz.

L = 47 mHC = 100 pF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 5 VC = 100 pF

A 100 pF capacitor is charged to 5 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in nJ.

C = 100 pFV0 = 5 VL = 47 mH
W = nJ
3.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 5
f1 = kHz
4.Medium
V4.7 kΩ1 mH2.2 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 1 mH and C = 2.2 nF. Find its quality factor Q.

R = 4.7 kΩL = 1 mHC = 2.2 nF
Q =
5.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 100 mHBW = 500 Hz
R = Ω
6.Hard
f|I|0.7071f0​ = ?100 kHz200 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 200 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 200 kHz
Q =

Answer key

  1. 1. f0 = 73.41 kHz
  2. 2. W = 1.25 nJ
  3. 3. f1 = 18.1 kHz
  4. 4. Q = 6.971
  5. 5. R = 314.2 Ω
  6. 6. Q = 1.414

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