Resonate Frequency of Parallel RLC Circuit

Discussion in 'Homework Help' started by p75213, Apr 17, 2012.

  1. p75213

    Thread Starter Member

    May 24, 2011
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    The question asks: Determine the resonant frequency of the circuit in Fig 14.28 (See attached).

    My question is:
    \begin{array}{l}<br />
 {\rm{How is }} \to {\omega _0}0.1 - \frac{{2{\omega _0}}}{{4 + 4\omega _0^2}} \\ <br />
 {\rm{derived from }} \to j\omega 0.1 + \frac{{2 - 2j\omega }}{{4 + 4{\omega ^2}}} \\ <br />
 \end{array}
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    The writer has equated the combined imaginary terms to equal zero at ωo [resonance].
     
    Last edited: Apr 17, 2012
  3. p75213

    Thread Starter Member

    May 24, 2011
    39
    0
    I understand that. However I still cant see how the 2nd equation is derived from the 1st.
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    OK - referring to attachment equations

    Y=0.1+j\omega 0.1+\frac{2-j \omega 2}{4+4\omega^2}=0.1+j\omega 0.1+\frac{2}{4+4\omega^2}-\frac{j \omega 2}{4+4\omega^2}

    The imaginary parts of Y (those with a 'j' operator) are ...

    imag[Y]=0.1 \omega -\frac{2 \omega }{4+4\omega^2}

    These equate to zero at ω=ωo

    Or when

    0.1 \omega_o -\frac{2 \omega_o }{4+4 {\omega_o}^2}=0

    The rest is algebraic manipulation to find ωo.
     
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