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 = 22 µH

An LC circuit with L = 22 µH must resonate at 20 kHz. Find the capacitance C in nF.

L = 22 µHf0 = 20 kHz
C = nF
2.Easy
tvC​iL​T/4T/2TV0​ = 1 VC = 10 µF

A 10 µF capacitor is charged to 1 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in µJ.

C = 10 µFV0 = 1 VL = 220 µH
W = µJ
3.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 5
f1 = kHz
4.Medium
V47 kΩ4.7 mH47 pF

A parallel RLC circuit has R = 47 kΩ, L = 4.7 mH and C = 47 pF. Find its quality factor Q.

R = 47 kΩL = 4.7 mHC = 47 pF
Q =
5.Hard
V22 Ω2.2 mH100 nF10 mA

A series RLC circuit (R = 22 Ω, L = 2.2 mH, C = 100 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 22 ΩL = 2.2 mHC = 100 nFIm = 10 mA
Ecycle = nJ
6.Hard
VR = ?100 mHC

A series resonant circuit uses a 100 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 100 mHBW = 50 kHz
R = Ω

Answer key

  1. 1. C = 2878 nF
  2. 2. W = 5 µJ
  3. 3. f1 = 90.5 kHz
  4. 4. Q = 4.7
  5. 5. Ecycle = 102.5 nJ
  6. 6. R = 31416 Ω

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