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
C = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 50 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 50 kHz
C = nF
2.Easy
C = 1 nF+−10 VL = 10 µHiL​

A 1 nF capacitor charged to 10 V is switched across an ideal 10 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 nFV0 = 10 VL = 10 µH
Imax = mA
3.Medium
V10 Ω470 µH2.2 nF

A series RLC circuit has R = 10 Ω, L = 470 µH and C = 2.2 nF. Find its quality factor Q.

R = 10 ΩL = 470 µHC = 2.2 nF
Q =
4.Medium
C = 4.7 nF+−3.75 VL = 470 µHiL​

A 4.7 nF capacitor charged to 15 V oscillates with an ideal 470 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3.75 V, in nJ.

C = 4.7 nFV0 = 15 VvC = 3.75 V
WL = nJ
5.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 22 µHBW = 100 kHz
R = Ω
6.Hard
VR = ?4.7 mHC

A series resonant circuit uses a 4.7 mH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 4.7 mHBW = 500 Hz
R = Ω

Answer key

  1. 1. C = 10.13 nF
  2. 2. Imax = 100 mA
  3. 3. Q = 46.22
  4. 4. WL = 495.7 nJ
  5. 5. R = 13.82 Ω
  6. 6. R = 14.77 Ω

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