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|0.7071100 kHzf1​f2​BW = 10 kHz

A resonance curve peaks at 100 kHz, and its half-power points are 10 kHz apart. Find the quality factor Q.

f0 = 100 kHzBW = 10 kHz
Q =
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = ?

A tuned circuit resonates at 1.6 MHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f0 = 1.6 MHzQ = 20
BW = kHz
3.Medium
V1 Ω4.7 mH220 nF

A series RLC circuit has R = 1 Ω, L = 4.7 mH and C = 220 nF. Find its quality factor Q.

R = 1 ΩL = 4.7 mHC = 220 nF
Q =
4.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
5.Hard
VR = ?100 mHC

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

L = 100 mHBW = 100 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?5 kHz6 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 6 kHz
Q =

Answer key

  1. 1. Q = 10
  2. 2. BW = 80 kHz
  3. 3. Q = 146.2
  4. 4. f1 = 18.1 kHz
  5. 5. R = 62832 Ω
  6. 6. Q = 5.477

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