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 = ?L = 22 µH

An LC circuit with L = 22 µH must resonate at 50 kHz. Find the capacitance C in nF.

L = 22 µHf0 = 50 kHz
C = nF
2.Easy
f|I|0.70711 MHzf1​f2​BW = ?

A tuned circuit resonates at 1 MHz and has a quality factor Q = 100. Find its bandwidth BW in kHz.

f0 = 1 MHzQ = 100
BW = kHz
3.Medium
V47 Ω470 µH470 pF

A series RLC circuit has R = 47 Ω, L = 470 µH and C = 470 pF. Find its bandwidth BW in kHz.

R = 47 ΩL = 470 µHC = 470 pF
BW = kHz
4.Medium
V2.2 kΩ220 µH1 nF

A parallel RLC circuit has R = 2.2 kΩ, L = 220 µH and C = 1 nF. Find its quality factor Q.

R = 2.2 kΩL = 220 µHC = 1 nF
Q =
5.Hard
C = 100 nFR = 1 ΩL = 10 mH

A charged 100 nF capacitor discharges through a 10 mH coil with a total series resistance of 1 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 = 100 nFR = 1 Ω
n =
6.Hard
f|I|0.7071f0​ = ?10 kHz25 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 25 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 25 kHz
Q =

Answer key

  1. 1. C = 460.6 nF
  2. 2. BW = 10 kHz
  3. 3. BW = 15.92 kHz
  4. 4. Q = 4.69
  5. 5. n = 69.77
  6. 6. Q = 1.054

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