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 = 107 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 107 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 107 kHz
Q =
2.Easy
C = 470 pFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 470 pF. Find its natural (resonance) frequency f0 in MHz.

L = 47 µHC = 470 pF
f0 = MHz
3.Medium
C = 470 pF+−4.8 VL = 100 mHiL​

A 470 pF capacitor charged to 24 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4.8 V, in nJ.

C = 470 pFV0 = 24 VvC = 4.8 V
WL = nJ
4.Medium
tvC​iL​T/4 = ?T/2TL = 220 µHC = 1 nF

In an ideal LC circuit with L = 220 µH and C = 1 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 220 µHC = 1 nF
t = µs
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 455 kHz and a bandwidth of 18.2 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 455 kHzBW = 18.2 kHz
C = nF
6.Hard
C = 47 nFr = 2 ΩL = 100 µH

A parallel tank circuit is made of a 47 nF capacitor and a 100 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 100 µHC = 47 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. Q = 100
  2. 2. f0 = 1.071 MHz
  3. 3. WL = 129.9 nJ
  4. 4. t = 0.7368 µs
  5. 5. C = 0.6996 nF
  6. 6. RD = 1.064 kΩ

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