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|0.707110.7 MHzf1​f2​BW = 535 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 535 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 535 kHz
Q =
2.Easy
tvC​iL​T/4T/2TV0​ = 24 VC = 1 µF

A 1 µF capacitor is charged to 24 V and then connected to an ideal 0.1 µH inductor. Find the total energy W that swings between them, in µJ.

C = 1 µFV0 = 24 VL = 0.1 µH
W = µJ
3.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 4
f1 = kHz
4.Medium
V220 Ω47 mH47 nF

A series RLC circuit has R = 220 Ω, L = 47 mH and C = 47 nF. Find its quality factor Q.

R = 220 ΩL = 47 mHC = 47 nF
Q =
5.Hard
C = 470 nFR = 20 ΩL = 22 mH

A charged 470 nF capacitor discharges through a 22 mH coil with a total series resistance of 20 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 = 22 mHC = 470 nFR = 20 Ω
n =
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 200 Hz. Find the capacitance C in nF.

R = 20 Ωf0 = 10 kHzBW = 200 Hz
C = nF

Answer key

  1. 1. Q = 20
  2. 2. W = 288 µJ
  3. 3. f1 = 17.66 kHz
  4. 4. Q = 4.545
  5. 5. n = 2.387
  6. 6. C = 15.92 nF

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