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 = 4.7 nFL = 22 µH

An ideal LC circuit has L = 22 µH and C = 4.7 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 µHC = 4.7 nF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 15 VC = 1 nF

A 1 nF 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 nJ.

C = 1 nFV0 = 15 VL = 220 µH
W = nJ
3.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 3
f1 = kHz
4.Medium
V22 Ω22 mH2.2 nF

A series RLC circuit has R = 22 Ω, L = 22 mH and C = 2.2 nF. Find its quality factor Q.

R = 22 ΩL = 22 mHC = 2.2 nF
Q =
5.Hard
VR = ?47 µHC

A series resonant circuit uses a 47 µH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 47 µHBW = 50 kHz
R = Ω
6.Hard
C = 470 nFr = 2 ΩL = 100 µH

A parallel tank circuit is made of a 470 nF capacitor and a 100 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 100 µHC = 470 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. f0 = 494.9 kHz
  2. 2. W = 112.5 nJ
  3. 3. f1 = 1.694 kHz
  4. 4. Q = 143.7
  5. 5. R = 14.77 Ω
  6. 6. RD = 0.1064 kΩ

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