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​ = 15 VC = 10 µF

A 10 µF capacitor is charged to 15 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in mJ.

C = 10 µFV0 = 15 VL = 220 µH
W = mJ
2.Easy
C = ?L = 22 µH

An LC circuit with L = 22 µH must resonate at 20 kHz. Find the capacitance C in nF.

L = 22 µHf0 = 20 kHz
C = nF
3.Medium
V220 Ω22 mH10 pF

A series RLC circuit has R = 220 Ω, L = 22 mH and C = 10 pF. Find its quality factor Q.

R = 220 ΩL = 22 mHC = 10 pF
Q =
4.Medium
V5 Ω470 µH22 nF

A series RLC circuit has R = 5 Ω, L = 470 µH and C = 22 nF. Find its bandwidth BW in kHz.

R = 5 ΩL = 470 µHC = 22 nF
BW = kHz
5.Hard
C = 1 nFR = 2 ΩL = 470 µH

A charged 1 nF capacitor discharges through a 470 µH coil with a total series resistance of 2 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 = 470 µHC = 1 nFR = 2 Ω
n =
6.Hard
C = 2.2 nFr = 1 ΩL = 470 µH

A parallel tank circuit is made of a 2.2 nF capacitor and a 470 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 = 470 µHC = 2.2 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. W = 1.125 mJ
  2. 2. C = 2878 nF
  3. 3. Q = 213.2
  4. 4. BW = 1.693 kHz
  5. 5. n = 75.63
  6. 6. RD = 213.6 kΩ

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