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 = 2.2 µF+−15 VL = 2.2 mHiL​

A 2.2 µF capacitor charged to 15 V is switched across an ideal 2.2 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 µFV0 = 15 VL = 2.2 mH
Imax = mA
2.Easy
C = ?L = 100 mH

An LC circuit with L = 100 mH must resonate at 10 kHz. Find the capacitance C in nF.

L = 100 mHf0 = 10 kHz
C = nF
3.Medium
C = 220 pF+−10 VL = 100 mHiL​

A 220 pF capacitor charged to 20 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 10 V, in nJ.

C = 220 pFV0 = 20 VvC = 10 V
WL = nJ
4.Medium
V1 kΩ1 mH4.7 nF

A parallel RLC circuit has R = 1 kΩ, L = 1 mH and C = 4.7 nF. Find its quality factor Q.

R = 1 kΩL = 1 mHC = 4.7 nF
Q =
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 200 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 200 kHzBW = 5 kHz
C = nF
6.Hard
C = 4.7 nFR = 20 ΩL = 22 mH

A charged 4.7 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 = 4.7 nFR = 20 Ω
n =

Answer key

  1. 1. Imax = 474.3 mA
  2. 2. C = 2.533 nF
  3. 3. WL = 33 nJ
  4. 4. Q = 2.168
  5. 5. C = 0.3979 nF
  6. 6. n = 23.87

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