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​ = 50 VC = 4.7 nF

A 4.7 nF capacitor is charged to 50 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in µJ.

C = 4.7 nFV0 = 50 VL = 4.7 mH
W = µJ
2.Easy
C = ?L = 10 mH

An LC circuit with L = 10 mH must resonate at 100 kHz. Find the capacitance C in nF.

L = 10 mHf0 = 100 kHz
C = nF
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 3
f1 = kHz
4.Medium
C = 100 nF+−2.5 VL = 22 µHiL​

A 100 nF capacitor charged to 10 V oscillates with an ideal 22 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2.5 V, in µJ.

C = 100 nFV0 = 10 VvC = 2.5 V
WL = µJ
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 10 kHz and a bandwidth of 400 Hz. Find the capacitance C in nF.

R = 50 Ωf0 = 10 kHzBW = 400 Hz
C = nF
6.Hard
V5 Ω100 µH10 nF10 mA

A series RLC circuit (R = 5 Ω, L = 100 µH, C = 10 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 100 µHC = 10 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. W = 5.875 µJ
  2. 2. C = 0.2533 nF
  3. 3. f1 = 423.6 kHz
  4. 4. WL = 4.688 µJ
  5. 5. C = 12.73 nF
  6. 6. Ecycle = 1.571 nJ

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