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 = 100 nF

A 100 nF capacitor is charged to 1 V and then connected to an ideal 10 mH inductor. Find the total energy W that swings between them, in nJ.

C = 100 nFV0 = 1 VL = 10 mH
W = nJ
2.Easy
C = ?L = 10 µH

An LC circuit with L = 10 µH must resonate at 200 kHz. Find the capacitance C in nF.

L = 10 µHf0 = 200 kHz
C = nF
3.Medium
V2 Ω1 µH47 nF

A series RLC circuit has R = 2 Ω, L = 1 µH and C = 47 nF. Find its quality factor Q.

R = 2 ΩL = 1 µHC = 47 nF
Q =
4.Medium
V100 Ω47 mH10 nF

A series RLC circuit has R = 100 Ω, L = 47 mH and C = 10 nF. Find its bandwidth BW in Hz.

R = 100 ΩL = 47 mHC = 10 nF
BW = Hz
5.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 100 mHBW = 20 kHz
R = Ω
6.Hard
VR = ?47 mHC

A series resonant circuit uses a 47 mH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 47 mHBW = 500 Hz
R = Ω

Answer key

  1. 1. W = 50 nJ
  2. 2. C = 63.33 nF
  3. 3. Q = 2.306
  4. 4. BW = 338.6 Hz
  5. 5. R = 12566 Ω
  6. 6. R = 147.7 Ω

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