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 = 220 pFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 220 pF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 220 pF
f0 = kHz
2.Easy
C = 47 nFL = 22 µH

An ideal LC circuit has L = 22 µH and C = 47 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 µHC = 47 nF
f0 = kHz
3.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
4.Medium
V2 Ω10 mH1 µF

A series RLC circuit has R = 2 Ω, L = 10 mH and C = 1 µF. Find its bandwidth BW in Hz.

R = 2 ΩL = 10 mHC = 1 µF
BW = Hz
5.Hard
C = 470 pFR = 5 ΩL = 1 mH

A charged 470 pF capacitor discharges through a 1 mH coil with a total series resistance of 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 = 1 mHC = 470 pFR = 5 Ω
n =
6.Hard
C = 470 pFr = 10 ΩL = 100 µH

A parallel tank circuit is made of a 470 pF capacitor and a 100 µH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 100 µHC = 470 pFr = 10 Ω
RD = kΩ

Answer key

  1. 1. f0 = 494.9 kHz
  2. 2. f0 = 156.5 kHz
  3. 3. f1 = 39.04 kHz
  4. 4. BW = 31.83 Hz
  5. 5. n = 64.37
  6. 6. RD = 21.28 kΩ

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