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 = 10 µF+−2 VL = 2.2 mHiL​

A 10 µF capacitor charged to 2 V is switched across an ideal 2.2 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 10 µFV0 = 2 VL = 2.2 mH
Imax = mA
2.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 =
3.Medium
V5 Ω47 µH1 nF

A series RLC circuit has R = 5 Ω, L = 47 µH and C = 1 nF. Find its quality factor Q.

R = 5 ΩL = 47 µHC = 1 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 mHC = 22 nF

In an ideal LC circuit with L = 22 mH and C = 22 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 = 22 mHC = 22 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?10 kHz25 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 25 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 25 kHz
Q =
6.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 470 µHBW = 2 kHz
R = Ω

Answer key

  1. 1. Imax = 134.8 mA
  2. 2. Q = 100
  3. 3. Q = 43.36
  4. 4. t = 34.56 µs
  5. 5. Q = 1.054
  6. 6. R = 5.906 Ω

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