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|0.70711.6 MHzf1​f2​BW = 64 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 64 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 64 kHz
Q =
2.Easy
f|I|0.7071455 kHzf1​f2​BW = 45.5 kHz

A resonance curve peaks at 455 kHz, and its half-power points are 45.5 kHz apart. Find the quality factor Q.

f0 = 455 kHzBW = 45.5 kHz
Q =
3.Medium
V2 Ω4.7 mH470 nF

A series RLC circuit has R = 2 Ω, L = 4.7 mH and C = 470 nF. Find its quality factor Q.

R = 2 ΩL = 4.7 mHC = 470 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 µHC = 10 µF

In an ideal LC circuit with L = 2.2 µH and C = 10 µF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 2.2 µHC = 10 µF
t = µs
5.Hard
f|I|0.7071f0​ = ?900 kHz1.125 MHzBW

The half-power frequencies of a resonance curve are 900 kHz and 1.125 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 900 kHzf2 = 1.125 MHz
Q =
6.Hard
f|I|0.7071f0​ = ?20 kHz21 kHzBW

The half-power frequencies of a resonance curve are 20 kHz and 21 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 20 kHzf2 = 21 kHz
Q =

Answer key

  1. 1. Q = 25
  2. 2. Q = 10
  3. 3. Q = 50
  4. 4. t = 7.368 µs
  5. 5. Q = 4.472
  6. 6. Q = 20.49

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