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 = 220 pFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 220 pF. Find its natural (resonance) frequency f0 in MHz.

L = 47 µHC = 220 pF
f0 = MHz
2.Easy
C = ?L = 220 µH

An LC circuit with L = 220 µH must resonate at 10 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 10 kHz
C = nF
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 4
f1 = kHz
4.Medium
V5 Ω47 mH47 nF

A series RLC circuit has R = 5 Ω, L = 47 mH and C = 47 nF. Find its quality factor Q.

R = 5 ΩL = 47 mHC = 47 nF
Q =
5.Hard
VR = ?1 mHC

A series resonant circuit uses a 1 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 1 mHBW = 50 kHz
R = Ω
6.Hard
V5 Ω220 µH470 pF10 mA

A series RLC circuit (R = 5 Ω, L = 220 µH, C = 470 pF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 220 µHC = 470 pFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. f0 = 1.565 MHz
  2. 2. C = 1151 nF
  3. 3. f1 = 4.414 kHz
  4. 4. Q = 200
  5. 5. R = 314.2 Ω
  6. 6. Ecycle = 0.5051 nJ

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