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 = 470 pFL = 10 mH

An ideal LC circuit has L = 10 mH and C = 470 pF. Find its natural (resonance) frequency f0 in kHz.

L = 10 mHC = 470 pF
f0 = kHz
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 5. Find its bandwidth BW in MHz.

f0 = 10.7 MHzQ = 5
BW = MHz
3.Medium
V100 Ω470 µH10 nF

A series RLC circuit has R = 100 Ω, L = 470 µH and C = 10 nF. Find its quality factor Q.

R = 100 ΩL = 470 µHC = 10 nF
Q =
4.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 1.5
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?100 kHz150 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 150 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 150 kHz
Q =
6.Hard
C = 220 pFR = 5 ΩL = 470 µH

A charged 220 pF capacitor discharges through a 470 µH coil with a total series resistance of 5 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 470 µHC = 220 pFR = 5 Ω
n =

Answer key

  1. 1. f0 = 73.41 kHz
  2. 2. BW = 2.14 MHz
  3. 3. Q = 2.168
  4. 4. f1 = 72.08 kHz
  5. 5. Q = 2.449
  6. 6. n = 64.5

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