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​ = 50 VC = 2.2 µF

A 2.2 µF capacitor is charged to 50 V and then connected to an ideal 470 µH inductor. Find the total energy W that swings between them, in mJ.

C = 2.2 µFV0 = 50 VL = 470 µH
W = mJ
2.Easy
C = 22 nFL = 47 mH

An ideal LC circuit has L = 47 mH and C = 22 nF. Find its natural (resonance) frequency f0 in kHz.

L = 47 mHC = 22 nF
f0 = kHz
3.Medium
V220 Ω220 µH220 pF

A series RLC circuit has R = 220 Ω, L = 220 µH and C = 220 pF. Find its bandwidth BW in kHz.

R = 220 ΩL = 220 µHC = 220 pF
BW = kHz
4.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 4
f1 = kHz
5.Hard
VR = ?220 µHC

A series resonant circuit uses a 220 µH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 220 µHBW = 10 kHz
R = Ω
6.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 5 kHz?

L = 100 mHBW = 5 kHz
R = Ω

Answer key

  1. 1. W = 2.75 mJ
  2. 2. f0 = 4.949 kHz
  3. 3. BW = 159.2 kHz
  4. 4. f1 = 441.4 kHz
  5. 5. R = 13.82 Ω
  6. 6. R = 3142 Ω

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