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|0.707110 kHzf1​f2​BW = 500 Hz

A resonance curve peaks at 10 kHz, and its half-power points are 500 Hz apart. Find the quality factor Q.

f0 = 10 kHzBW = 500 Hz
Q =
2.Easy
C = ?L = 470 µH

An LC circuit with L = 470 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 470 µHf0 = 1 MHz
C = nF
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 3
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 10 µHC = 10 µF

In an ideal LC circuit with L = 10 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 = 10 µHC = 10 µF
t = µs
5.Hard
V22 Ω10 mH47 nF100 mA

A series RLC circuit (R = 22 Ω, L = 10 mH, C = 47 nF) is driven at resonance with a current amplitude of 100 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 10 mHC = 47 nFIm = 100 mA
Ecycle = µJ
6.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 10 kHz and a bandwidth of 1 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 10 kHzBW = 1 kHz
C = nF

Answer key

  1. 1. Q = 20
  2. 2. C = 0.05389 nF
  3. 3. f1 = 4.236 kHz
  4. 4. t = 15.71 µs
  5. 5. Ecycle = 14.98 µJ
  6. 6. C = 15.92 nF

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