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|0.70711 MHzf1​f2​BW = ?

A tuned circuit resonates at 1 MHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 1 MHzQ = 8
BW = kHz
2.Easy
C = 1 nFL = 4.7 mH

An ideal LC circuit has L = 4.7 mH and C = 1 nF. Find its natural (resonance) frequency f0 in kHz.

L = 4.7 mHC = 1 nF
f0 = kHz
3.Medium
V22 Ω22 mH220 nF

A series RLC circuit has R = 22 Ω, L = 22 mH and C = 220 nF. Find its bandwidth BW in Hz.

R = 22 ΩL = 22 mHC = 220 nF
BW = Hz
4.Medium
V1 Ω2.2 mH470 nF

A series RLC circuit has R = 1 Ω, L = 2.2 mH and C = 470 nF. Find its bandwidth BW in Hz.

R = 1 ΩL = 2.2 mHC = 470 nF
BW = Hz
5.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 22 µHBW = 50 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?8 kHz12.8 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 12.8 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 12.8 kHz
Q =

Answer key

  1. 1. BW = 125 kHz
  2. 2. f0 = 73.41 kHz
  3. 3. BW = 159.2 Hz
  4. 4. BW = 72.34 Hz
  5. 5. R = 6.912 Ω
  6. 6. Q = 2.108

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