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​ = 15 VC = 10 µF

A 10 µF capacitor is charged to 15 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in mJ.

C = 10 µFV0 = 15 VL = 220 µH
W = mJ
2.Easy
C = 47 nFL = 22 µH

An ideal LC circuit has L = 22 µH and C = 47 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 µHC = 47 nF
f0 = kHz
3.Medium
V220 Ω4.7 mH100 pF

A series RLC circuit has R = 220 Ω, L = 4.7 mH and C = 100 pF. Find its quality factor Q.

R = 220 ΩL = 4.7 mHC = 100 pF
Q =
4.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 2
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?900 kHz1.35 MHzBW

The half-power frequencies of a resonance curve are 900 kHz and 1.35 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 900 kHzf2 = 1.35 MHz
Q =
6.Hard
f|I|0.7071f0​ = ?5 kHz5.5 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 5.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 5.5 kHz
Q =

Answer key

  1. 1. W = 1.125 mJ
  2. 2. f0 = 156.5 kHz
  3. 3. Q = 31.16
  4. 4. f1 = 15.62 kHz
  5. 5. Q = 2.449
  6. 6. Q = 10.49

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