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|0.70711 MHzf1​f2​BW = 12.5 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 12.5 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 12.5 kHz
Q =
2.Easy
C = ?L = 100 mH

An LC circuit with L = 100 mH must resonate at 1 kHz. Find the capacitance C in nF.

L = 100 mHf0 = 1 kHz
C = nF
3.Medium
C = 10 µF+−10 VL = 470 µHiL​

A 10 µF capacitor charged to 20 V oscillates with an ideal 470 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 10 V, in mJ.

C = 10 µFV0 = 20 VvC = 10 V
WL = mJ
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 µHC = 2.2 µF

In an ideal LC circuit with L = 1 µH and C = 2.2 µF, 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 = 1 µHC = 2.2 µF
t = µs
5.Hard
C = 4.7 nFr = 5 ΩL = 220 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 220 µH coil with a winding resistance of 5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 220 µHC = 4.7 nFr = 5 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?10 kHz10.5 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 10.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 10.5 kHz
Q =

Answer key

  1. 1. Q = 80
  2. 2. C = 253.3 nF
  3. 3. WL = 1.5 mJ
  4. 4. t = 2.33 µs
  5. 5. RD = 9.362 kΩ
  6. 6. Q = 20.49

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