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 = 12.5 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 12.5 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 12.5 Hz
Q =
2.Easy
f|I|0.70711 MHzf1​f2​BW = 125 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 125 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 125 kHz
Q =
3.Medium
V100 Ω22 mH470 nF

A series RLC circuit has R = 100 Ω, L = 22 mH and C = 470 nF. Find its quality factor Q.

R = 100 ΩL = 22 mHC = 470 nF
Q =
4.Medium
V47 kΩ22 mH470 pF

A parallel RLC circuit has R = 47 kΩ, L = 22 mH and C = 470 pF. Find its quality factor Q.

R = 47 kΩL = 22 mHC = 470 pF
Q =
5.Hard
V2 Ω470 µH10 nF50 mA

A series RLC circuit (R = 2 Ω, L = 470 µH, C = 10 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 470 µHC = 10 nFIm = 50 mA
Ecycle = nJ
6.Hard
C = 10 nFR = 10 ΩL = 2.2 mH

A charged 10 nF capacitor discharges through a 2.2 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 = 2.2 mHC = 10 nFR = 10 Ω
n =

Answer key

  1. 1. Q = 80
  2. 2. Q = 8
  3. 3. Q = 2.164
  4. 4. Q = 6.87
  5. 5. Ecycle = 34.05 nJ
  6. 6. n = 10.35

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