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Phasors and Practical Impedances

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Date Posted: 7/21/2008 11:45:01 PM  Status: Live
Phasors and Practical Impedances
Course Textbook Chapter Problem
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Question Details:

Capacitors and inductors have been shown as ideal elements with impedances: ZC and ZL

Z(L) = V(L)/I(L) = jωL  & Z(C) = V(C)/I(C)= 1/jωC
A more practical mode of these components is shown in the figure below
a) Find the impedances of the practical components described by the figure. Compare
with the ideal impedances above.

b) Sketch the (magnitude only) Bode plot (plot of 20 log(||Z(jω)||) .vs. log(ω)) of the
ideal and practical components. Use as values for the parameters:
L = 0.08[H], R = 0.1[Ω], C = 0.1[μF], R1 = 1[MΩ].

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Date Posted: 7/22/2008 3:37:22 AM  Status: Live
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Response:
 a)        
                  
 
        As the practical inductor contains a resistor and inductor in series. The ideal inductor contains only imaginary part where as practical inductor contains both real and imaginary.
                        ( Practical )
                              ( Ideal )
 
                  
 
         The practical capacitor contains a resistor and capacitor  in parallel. The ideal capacitor contains only imaginary part where as practical capacitor contains both real and imaginary.
               
                        ( Practical )
                                ( Ideal )
   b)
         Substitute values of R , L , C , R1
               
         Magnitude
                                                       ( Ideal )
                                 ( Practical )
         Magnitude
               
                                                 ( Ideal )
                                               ( Practical )
 
         By the magnitude equations we can sketch the bode plot by taking the logarithm of given magnitude values.
 
 
 
 
Hope this helps you.............



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