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 = 470 nF+−9 VL = 10 mHiL​

A 470 nF capacitor charged to 9 V is switched across an ideal 10 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 nFV0 = 9 VL = 10 mH
Imax = mA
2.Easy
f|I|0.70712 kHzf1​f2​BW = 50 Hz

A resonance curve peaks at 2 kHz, and its half-power points are 50 Hz apart. Find the quality factor Q.

f0 = 2 kHzBW = 50 Hz
Q =
3.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 1.5
f1 = kHz
4.Medium
C = 100 nF+−6 VL = 2.2 mHiL​

A 100 nF capacitor charged to 10 V oscillates with an ideal 2.2 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in µJ.

C = 100 nFV0 = 10 VvC = 6 V
WL = µJ
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 1 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 10 kHzBW = 1 kHz
C = nF
6.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 100 mHBW = 1 kHz
R = Ω

Answer key

  1. 1. Imax = 61.7 mA
  2. 2. Q = 40
  3. 3. f1 = 14.42 kHz
  4. 4. WL = 3.2 µJ
  5. 5. C = 79.58 nF
  6. 6. R = 628.3 Ω

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