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|0.70711 kHzf1​f2​BW = ?

A tuned circuit resonates at 1 kHz and has a quality factor Q = 12. Find its bandwidth BW in Hz.

f0 = 1 kHzQ = 12
BW = Hz
2.Easy
tvC​iL​T/4T/2TV0​ = 5 VC = 2.2 nF

A 2.2 nF capacitor is charged to 5 V and then connected to an ideal 100 µH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 5 VL = 100 µH
W = nJ
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2
f1 = kHz
4.Medium
V10 Ω2.2 mH100 nF

A series RLC circuit has R = 10 Ω, L = 2.2 mH and C = 100 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 2.2 mHC = 100 nF
BW = Hz
5.Hard
C = 1 µFR = 0.5 ΩL = 10 mH

A charged 1 µF capacitor discharges through a 10 mH coil with a total series resistance of 0.5 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 = 10 mHC = 1 µFR = 0.5 Ω
n =
6.Hard
V5 Ω10 mH1 µF500 mA

A series RLC circuit (R = 5 Ω, L = 10 mH, C = 1 µF) is driven at resonance with a current amplitude of 500 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 5 ΩL = 10 mHC = 1 µFIm = 500 mA
Ecycle = µJ

Answer key

  1. 1. BW = 83.33 Hz
  2. 2. W = 27.5 nJ
  3. 3. f1 = 3.904 kHz
  4. 4. BW = 723.4 Hz
  5. 5. n = 44.13
  6. 6. Ecycle = 392.7 µJ

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