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​ = 20 VC = 47 nF

A 47 nF capacitor is charged to 20 V and then connected to an ideal 100 µH inductor. Find the total energy W that swings between them, in µJ.

C = 47 nFV0 = 20 VL = 100 µH
W = µJ
2.Easy
tvC​iL​T/4T/2TV0​ = 2 VC = 10 µF

A 10 µF capacitor is charged to 2 V and then connected to an ideal 2.2 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 2 VL = 2.2 µH
W = µJ
3.Medium
V10 kΩ100 µH4.7 nF

A parallel RLC circuit has R = 10 kΩ, L = 100 µH and C = 4.7 nF. Find its quality factor Q.

R = 10 kΩL = 100 µHC = 4.7 nF
Q =
4.Medium
V47 Ω220 µH22 nF

A series RLC circuit has R = 47 Ω, L = 220 µH and C = 22 nF. Find its quality factor Q.

R = 47 ΩL = 220 µHC = 22 nF
Q =
5.Hard
f|I|0.7071f0​ = ?50 kHz55 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 55 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 55 kHz
Q =
6.Hard
f|I|0.7071f0​ = ?50 kHz75 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 75 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 75 kHz
Q =

Answer key

  1. 1. W = 9.4 µJ
  2. 2. W = 20 µJ
  3. 3. Q = 68.56
  4. 4. Q = 2.128
  5. 5. Q = 10.49
  6. 6. Q = 2.449

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