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 = 220 pFL = 4.7 mH

An ideal LC circuit has L = 4.7 mH and C = 220 pF. Find its natural (resonance) frequency f0 in kHz.

L = 4.7 mHC = 220 pF
f0 = kHz
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 1 MHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 1 MHz
C = nF
3.Medium
C = 1 µF+−4 VL = 22 mHiL​

A 1 µF capacitor charged to 5 V oscillates with an ideal 22 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4 V, in µJ.

C = 1 µFV0 = 5 VvC = 4 V
WL = µJ
4.Medium
f|I|0.7071200 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 200 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 200 kHzQ = 1.5
f1 = kHz
5.Hard
C = 10 nFr = 10 ΩL = 22 mH

A parallel tank circuit is made of a 10 nF capacitor and a 22 mH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 22 mHC = 10 nFr = 10 Ω
RD = kΩ
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 200 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 200 kHzBW = 4 kHz
C = nF

Answer key

  1. 1. f0 = 156.5 kHz
  2. 2. C = 0.01151 nF
  3. 3. WL = 4.5 µJ
  4. 4. f1 = 144.2 kHz
  5. 5. RD = 220 kΩ
  6. 6. C = 3.183 nF

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