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 500 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 500 kHz
C = nF
2.Easy
C = 220 pFL = 100 µH

An ideal LC circuit has L = 100 µH and C = 220 pF. Find its natural (resonance) frequency f0 in MHz.

L = 100 µHC = 220 pF
f0 = MHz
3.Medium
V47 Ω10 mH220 pF

A series RLC circuit has R = 47 Ω, L = 10 mH and C = 220 pF. Find its quality factor Q.

R = 47 ΩL = 10 mHC = 220 pF
Q =
4.Medium
C = 100 nF+−2.4 VL = 100 mHiL​

A 100 nF capacitor charged to 12 V oscillates with an ideal 100 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2.4 V, in µJ.

C = 100 nFV0 = 12 VvC = 2.4 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?2 kHz5 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 5 kHz
Q =
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 = 0.1013 nF
  2. 2. f0 = 1.073 MHz
  3. 3. Q = 143.4
  4. 4. WL = 6.912 µJ
  5. 5. Q = 1.054
  6. 6. R = 14.77 Ω

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