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​ = 9 VC = 47 nF

A 47 nF capacitor is charged to 9 V and then connected to an ideal 100 µH inductor. Find the total energy W that swings between them, in µJ.

C = 47 nFV0 = 9 VL = 100 µH
W = µJ
2.Easy
f|I|0.70711 MHzf1​f2​BW = 25 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 25 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 25 kHz
Q =
3.Medium
C = 1 µF+−18 VL = 100 µHiL​

A 1 µF capacitor charged to 24 V oscillates with an ideal 100 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 18 V, in µJ.

C = 1 µFV0 = 24 VvC = 18 V
WL = µJ
4.Medium
f|I|0.7071200 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 200 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 200 kHzQ = 3
f1 = kHz
5.Hard
V2 Ω22 µH47 nF200 mA

A series RLC circuit (R = 2 Ω, L = 22 µH, C = 47 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 22 µHC = 47 nFIm = 200 mA
Ecycle = nJ
6.Hard
f|I|0.7071f0​ = ?20 kHz24 kHzBW

The half-power frequencies of a resonance curve are 20 kHz and 24 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 20 kHzf2 = 24 kHz
Q =

Answer key

  1. 1. W = 1.903 µJ
  2. 2. Q = 40
  3. 3. WL = 126 µJ
  4. 4. f1 = 169.4 kHz
  5. 5. Ecycle = 255.6 nJ
  6. 6. Q = 5.477

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