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 = 10 pFL = 47 mH

An ideal LC circuit has L = 47 mH and C = 10 pF. Find its natural (resonance) frequency f0 in kHz.

L = 47 mHC = 10 pF
f0 = kHz
2.Easy
C = 47 nFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 47 nF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 47 nF
f0 = kHz
3.Medium
V47 Ω47 mH47 nF

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

R = 47 ΩL = 47 mHC = 47 nF
Q =
4.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 5
f1 = Hz
5.Hard
VR = ?2.2 mHC

A series resonant circuit uses a 2.2 mH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 2.2 mHBW = 500 Hz
R = Ω
6.Hard
V1 Ω4.7 mH1 µF50 mA

A series RLC circuit (R = 1 Ω, L = 4.7 mH, C = 1 µF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 4.7 mHC = 1 µFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. f0 = 232.2 kHz
  2. 2. f0 = 33.86 kHz
  3. 3. Q = 21.28
  4. 4. f1 = 905 Hz
  5. 5. R = 6.912 Ω
  6. 6. Ecycle = 538.4 nJ

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