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 = 220 µH

An LC circuit with L = 220 µH must resonate at 455 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 455 kHz
C = nF
2.Easy
C = 4.7 nFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 4.7 nF. Find its natural (resonance) frequency f0 in kHz.

L = 47 µHC = 4.7 nF
f0 = kHz
3.Medium
V22 kΩ47 µH1 nF

A parallel RLC circuit has R = 22 kΩ, L = 47 µH and C = 1 nF. Find its quality factor Q.

R = 22 kΩL = 47 µHC = 1 nF
Q =
4.Medium
C = 47 nF+−1 VL = 10 µHiL​

A 47 nF capacitor charged to 5 V oscillates with an ideal 10 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1 V, in nJ.

C = 47 nFV0 = 5 VvC = 1 V
WL = nJ
5.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 10 kHz and a bandwidth of 200 Hz. Find the capacitance C in nF.

R = 100 Ωf0 = 10 kHzBW = 200 Hz
C = nF
6.Hard
V2 Ω100 µH10 nF100 mA

A series RLC circuit (R = 2 Ω, L = 100 µH, C = 10 nF) is driven at resonance with a current amplitude of 100 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 100 µHC = 10 nFIm = 100 mA
Ecycle = nJ

Answer key

  1. 1. C = 0.5562 nF
  2. 2. f0 = 338.6 kHz
  3. 3. Q = 101.5
  4. 4. WL = 564 nJ
  5. 5. C = 3.183 nF
  6. 6. Ecycle = 62.83 nJ

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