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
tvC​iL​T/4T/2TV0​ = 1 VC = 10 µF

A 10 µF capacitor is charged to 1 V and then connected to an ideal 0.1 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 1 VL = 0.1 µH
W = µJ
2.Easy
f|I|0.7071500 kHzf1​f2​BW = ?

A tuned circuit resonates at 500 kHz and has a quality factor Q = 40. Find its bandwidth BW in kHz.

f0 = 500 kHzQ = 40
BW = kHz
3.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 1.5
f1 = kHz
4.Medium
C = 220 nF+−1.2 VL = 220 µHiL​

A 220 nF capacitor charged to 6 V oscillates with an ideal 220 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.2 V, in µJ.

C = 220 nFV0 = 6 VvC = 1.2 V
WL = µJ
5.Hard
C = 100 nFr = 2 ΩL = 22 µH

A parallel tank circuit is made of a 100 nF capacitor and a 22 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 = 22 µHC = 100 nFr = 2 Ω
RD = kΩ
6.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 470 µHBW = 20 kHz
R = Ω

Answer key

  1. 1. W = 5 µJ
  2. 2. BW = 12.5 kHz
  3. 3. f1 = 7.208 kHz
  4. 4. WL = 3.802 µJ
  5. 5. RD = 0.11 kΩ
  6. 6. R = 59.06 Ω

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