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 = 47 nFL = 100 mH

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

L = 100 mHC = 47 nF
f0 = kHz
2.Easy
f|I|0.7071500 kHzf1​f2​BW = 20 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 20 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 20 kHz
Q =
3.Medium
V10 Ω100 mH100 nF

A series RLC circuit has R = 10 Ω, L = 100 mH and C = 100 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 100 mHC = 100 nF
BW = Hz
4.Medium
V220 Ω47 mH220 pF

A series RLC circuit has R = 220 Ω, L = 47 mH and C = 220 pF. Find its quality factor Q.

R = 220 ΩL = 47 mHC = 220 pF
Q =
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 100 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 100 kHzBW = 4 kHz
C = nF
6.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

Answer key

  1. 1. f0 = 2.322 kHz
  2. 2. Q = 25
  3. 3. BW = 15.92 Hz
  4. 4. Q = 66.44
  5. 5. C = 1.273 nF
  6. 6. R = 13.82 Ω

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