Resonate Frequency of Parallel RLC Circuit

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

1. p75213 Thread Starter Active Member

May 24, 2011
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0
The question asks: Determine the resonant frequency of the circuit in Fig 14.28 (See attached).

My question is:
$\begin{array}{l}
{\rm{How is }} \to {\omega _0}0.1 - \frac{{2{\omega _0}}}{{4 + 4\omega _0^2}} \\
{\rm{derived from }} \to j\omega 0.1 + \frac{{2 - 2j\omega }}{{4 + 4{\omega ^2}}} \\
\end{array}$

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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 Active Member

May 24, 2011
70
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
790
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.