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 = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 8. Find its bandwidth BW in MHz.

f0 = 10.7 MHzQ = 8
BW = MHz
2.Easy
C = 100 pF+−20 VL = 10 mHiL​

A 100 pF capacitor charged to 20 V is switched across an ideal 10 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 pFV0 = 20 VL = 10 mH
Imax = mA
3.Medium
V2 Ω1 mH2.2 µF

A series RLC circuit has R = 2 Ω, L = 1 mH and C = 2.2 µF. Find its bandwidth BW in Hz.

R = 2 ΩL = 1 mHC = 2.2 µF
BW = Hz
4.Medium
V2 Ω470 µH470 nF

A series RLC circuit has R = 2 Ω, L = 470 µH and C = 470 nF. Find its bandwidth BW in Hz.

R = 2 ΩL = 470 µHC = 470 nF
BW = Hz
5.Hard
f|I|0.7071f0​ = ?50 kHz60 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 60 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 60 kHz
Q =
6.Hard
C = 470 nFR = 10 ΩL = 2.2 mH

A charged 470 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 = 470 nFR = 10 Ω
n =

Answer key

  1. 1. BW = 1.337 MHz
  2. 2. Imax = 2 mA
  3. 3. BW = 318.3 Hz
  4. 4. BW = 677.3 Hz
  5. 5. Q = 5.477
  6. 6. n = 1.51

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