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 = ?L = 47 µH

An LC circuit with L = 47 µH must resonate at 20 kHz. Find the capacitance C in nF.

L = 47 µHf0 = 20 kHz
C = nF
2.Easy
f|I|0.7071100 kHzf1​f2​BW = 1 kHz

A resonance curve peaks at 100 kHz, and its half-power points are 1 kHz apart. Find the quality factor Q.

f0 = 100 kHzBW = 1 kHz
Q =
3.Medium
C = 470 pF+−3.75 VL = 220 µHiL​

A 470 pF capacitor charged to 5 V oscillates with an ideal 220 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3.75 V, in nJ.

C = 470 pFV0 = 5 VvC = 3.75 V
WL = nJ
4.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 2
f1 = kHz
5.Hard
V5 Ω22 mH470 nF100 mA

A series RLC circuit (R = 5 Ω, L = 22 mH, C = 470 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 = 5 ΩL = 22 mHC = 470 nFIm = 100 mA
Ecycle = µJ
6.Hard
C = 22 nFR = 10 ΩL = 4.7 mH

A charged 22 nF capacitor discharges through a 4.7 mH coil with a total series resistance of 10 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 4.7 mHC = 22 nFR = 10 Ω
n =

Answer key

  1. 1. C = 1347 nF
  2. 2. Q = 100
  3. 3. WL = 2.57 nJ
  4. 4. f1 = 7.808 kHz
  5. 5. Ecycle = 15.97 µJ
  6. 6. n = 10.2

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