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|0.70715 kHzf1​f2​BW = ?

A tuned circuit resonates at 5 kHz and has a quality factor Q = 25. Find its bandwidth BW in Hz.

f0 = 5 kHzQ = 25
BW = Hz
2.Easy
tvC​iL​T/4T/2TV0​ = 15 VC = 10 nF

A 10 nF capacitor is charged to 15 V and then connected to an ideal 22 mH inductor. Find the total energy W that swings between them, in µJ.

C = 10 nFV0 = 15 VL = 22 mH
W = µJ
3.Medium
C = 470 pF+−15 VL = 220 µHiL​

A 470 pF capacitor charged to 20 V oscillates with an ideal 220 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 15 V, in nJ.

C = 470 pFV0 = 20 VvC = 15 V
WL = nJ
4.Medium
V5 Ω10 µH10 nF

A series RLC circuit has R = 5 Ω, L = 10 µH and C = 10 nF. Find its quality factor Q.

R = 5 ΩL = 10 µHC = 10 nF
Q =
5.Hard
f|I|0.7071f0​ = ?400 kHz1 MHzBW

The half-power frequencies of a resonance curve are 400 kHz and 1 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 1 MHz
Q =
6.Hard
C = 4.7 nFr = 1 ΩL = 10 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 10 µH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 10 µHC = 4.7 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. BW = 200 Hz
  2. 2. W = 1.125 µJ
  3. 3. WL = 41.13 nJ
  4. 4. Q = 6.325
  5. 5. Q = 1.054
  6. 6. RD = 2.128 kΩ

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