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 = 1 µFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 1 µF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 1 µF
f0 = kHz
2.Easy
f|I|0.707150 kHzf1​f2​BW = 500 Hz

A resonance curve peaks at 50 kHz, and its half-power points are 500 Hz apart. Find the quality factor Q.

f0 = 50 kHzBW = 500 Hz
Q =
3.Medium
V1 kΩ2.2 mH100 nF

A parallel RLC circuit has R = 1 kΩ, L = 2.2 mH and C = 100 nF. Find its quality factor Q.

R = 1 kΩL = 2.2 mHC = 100 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 mHC = 470 pF

In an ideal LC circuit with L = 2.2 mH and C = 470 pF, 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 mHC = 470 pF
t = µs
5.Hard
V1 Ω4.7 mH470 nF10 mA

A series RLC circuit (R = 1 Ω, L = 4.7 mH, C = 470 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 4.7 mHC = 470 nFIm = 10 mA
Ecycle = nJ
6.Hard
V2 Ω220 µH2.2 µF10 mA

A series RLC circuit (R = 2 Ω, L = 220 µH, C = 2.2 µF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 220 µHC = 2.2 µFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. f0 = 7.341 kHz
  2. 2. Q = 100
  3. 3. Q = 6.742
  4. 4. t = 1.597 µs
  5. 5. Ecycle = 14.77 nJ
  6. 6. Ecycle = 13.82 nJ

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