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 = 100 nF+−20 VL = 100 mHiL​

A 100 nF capacitor charged to 20 V is switched across an ideal 100 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 nFV0 = 20 VL = 100 mH
Imax = mA
2.Easy
C = 2.2 nF+−12 VL = 22 mHiL​

A 2.2 nF capacitor charged to 12 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 nFV0 = 12 VL = 22 mH
Imax = mA
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 3
f1 = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 100 mHC = 47 nF

In an ideal LC circuit with L = 100 mH and C = 47 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 = 100 mHC = 47 nF
t = µs
5.Hard
V2 Ω470 µH100 nF200 mA

A series RLC circuit (R = 2 Ω, L = 470 µH, C = 100 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 2 ΩL = 470 µHC = 100 nFIm = 200 mA
Ecycle = µJ
6.Hard
VR = ?4.7 mHC

A series resonant circuit uses a 4.7 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 4.7 mHBW = 50 kHz
R = Ω

Answer key

  1. 1. Imax = 20 mA
  2. 2. Imax = 3.795 mA
  3. 3. f1 = 847.1 Hz
  4. 4. t = 107.7 µs
  5. 5. Ecycle = 1.723 µJ
  6. 6. R = 1477 Ω

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