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|0.7071500 kHzf1​f2​BW = 12.5 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 12.5 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 12.5 kHz
Q =
2.Easy
C = 10 µFL = 2.2 mH

An ideal LC circuit has L = 2.2 mH and C = 10 µF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 mHC = 10 µF
f0 = kHz
3.Medium
V2 Ω47 µH10 nF

A series RLC circuit has R = 2 Ω, L = 47 µH and C = 10 nF. Find its bandwidth BW in kHz.

R = 2 ΩL = 47 µHC = 10 nF
BW = kHz
4.Medium
C = 100 nF+−12 VL = 100 mHiL​

A 100 nF capacitor charged to 24 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 12 V, in µJ.

C = 100 nFV0 = 24 VvC = 12 V
WL = µJ
5.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 =
6.Hard
C = 22 nFr = 1 ΩL = 10 µH

A parallel tank circuit is made of a 22 nF capacitor and a 10 µH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 10 µHC = 22 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. Q = 40
  2. 2. f0 = 1.073 kHz
  3. 3. BW = 6.773 kHz
  4. 4. WL = 21.6 µJ
  5. 5. n = 10.2
  6. 6. RD = 0.4545 kΩ

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