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|0.70715 kHzf1​f2​BW = 50 Hz

A resonance curve peaks at 5 kHz, and its half-power points are 50 Hz apart. Find the quality factor Q.

f0 = 5 kHzBW = 50 Hz
Q =
2.Easy
C = 100 nFL = 2.2 mH

An ideal LC circuit has L = 2.2 mH and C = 100 nF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 mHC = 100 nF
f0 = kHz
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 3
f1 = Hz
4.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 3
f1 = kHz
5.Hard
C = 220 nFR = 1 ΩL = 22 µH

A charged 220 nF capacitor discharges through a 22 µH coil with a total series resistance of 1 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 = 22 µHC = 220 nFR = 1 Ω
n =
6.Hard
f|I|0.7071f0​ = ?8 kHz9.6 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 9.6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 9.6 kHz
Q =

Answer key

  1. 1. Q = 100
  2. 2. f0 = 10.73 kHz
  3. 3. f1 = 847.1 Hz
  4. 4. f1 = 8.471 kHz
  5. 5. n = 2.206
  6. 6. Q = 5.477

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