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​ = 10 VC = 1 µF

A 1 µF capacitor is charged to 10 V and then connected to an ideal 0.47 µH inductor. Find the total energy W that swings between them, in µJ.

C = 1 µFV0 = 10 VL = 0.47 µH
W = µJ
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = 320 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 320 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 320 kHz
Q =
3.Medium
V1 Ω470 µH470 nF

A series RLC circuit has R = 1 Ω, L = 470 µH and C = 470 nF. Find its quality factor Q.

R = 1 ΩL = 470 µHC = 470 nF
Q =
4.Medium
V47 kΩ2.2 mH47 pF

A parallel RLC circuit has R = 47 kΩ, L = 2.2 mH and C = 47 pF. Find its quality factor Q.

R = 47 kΩL = 2.2 mHC = 47 pF
Q =
5.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 50 kHzBW = 2 kHz
C = nF
6.Hard
f|I|0.7071f0​ = ?8 kHz8.4 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 8.4 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 8.4 kHz
Q =

Answer key

  1. 1. W = 50 µJ
  2. 2. Q = 5
  3. 3. Q = 31.62
  4. 4. Q = 6.87
  5. 5. C = 25.46 nF
  6. 6. Q = 20.49

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