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|0.707150 kHzf1​f2​BW = 2.5 kHz

A resonance curve peaks at 50 kHz, and its half-power points are 2.5 kHz apart. Find the quality factor Q.

f0 = 50 kHzBW = 2.5 kHz
Q =
2.Easy
C = 2.2 nFL = 47 mH

An ideal LC circuit has L = 47 mH and C = 2.2 nF. Find its natural (resonance) frequency f0 in kHz.

L = 47 mHC = 2.2 nF
f0 = kHz
3.Medium
V5 Ω220 µH100 nF

A series RLC circuit has R = 5 Ω, L = 220 µH and C = 100 nF. Find its quality factor Q.

R = 5 ΩL = 220 µHC = 100 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 µHC = 100 nF

In an ideal LC circuit with L = 1 µH and C = 100 nF, 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 = 1 µHC = 100 nF
t = µs
5.Hard
V5 Ω47 µH10 nF200 mA

A series RLC circuit (R = 5 Ω, L = 47 µH, C = 10 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 47 µHC = 10 nFIm = 200 mA
Ecycle = nJ
6.Hard
f|I|0.7071f0​ = ?2 kHz4 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 4 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 4 kHz
Q =

Answer key

  1. 1. Q = 20
  2. 2. f0 = 15.65 kHz
  3. 3. Q = 9.381
  4. 4. t = 0.4967 µs
  5. 5. Ecycle = 430.8 nJ
  6. 6. Q = 1.414

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