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
tvC​iL​T/4T/2TV0​ = 10 VC = 47 nF

A 47 nF capacitor is charged to 10 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in µJ.

C = 47 nFV0 = 10 VL = 47 mH
W = µJ
2.Easy
C = 1 nF+−9 VL = 100 µHiL​

A 1 nF capacitor charged to 9 V is switched across an ideal 100 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 nFV0 = 9 VL = 100 µH
Imax = mA
3.Medium
tvC​iL​T/4 = ?T/2TL = 470 µHC = 10 µF

In an ideal LC circuit with L = 470 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 = 470 µHC = 10 µF
t = µs
4.Medium
f|I|0.707150 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 50 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 50 kHzQ = 2
f1 = kHz
5.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 50 kHzBW = 2 kHz
C = nF
6.Hard
V5 Ω47 µH100 nF50 mA

A series RLC circuit (R = 5 Ω, L = 47 µH, C = 100 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 47 µHC = 100 nFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. W = 2.35 µJ
  2. 2. Imax = 28.46 mA
  3. 3. t = 107.7 µs
  4. 4. f1 = 39.04 kHz
  5. 5. C = 1.273 nF
  6. 6. Ecycle = 85.14 nJ

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