anyone knows use Laplace to find ZT and IT?

Discussion in 'Homework Help' started by kuangmao, Apr 29, 2009.

  1. kuangmao

    Thread Starter New Member

    Apr 29, 2009
    3
    0
    anyone knows use Laplace to find ZT and IT?
    PLEASE.....IT'S DUE TOMORROW................
    SAD.JPG

    Laplace.JPG

    sd.jpg
    View attachment it.bmp
     
    Last edited: Apr 30, 2009
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    kuangmao,

    Show us your attempt at a solution.

    Ratch
     
  3. kuangmao

    Thread Starter New Member

    Apr 29, 2009
    3
    0
    find the total impedance and the total current using laplace.
     
  4. kuangmao

    Thread Starter New Member

    Apr 29, 2009
    3
    0
    and please show me the work steps
    thanks so much guys.
     
  5. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    kuangmao,

    Your result Zt = (2*(3*s^2+14*s+7))/(s^2+5*s+2) is correct

    Dividing Zt into voltage 6/s gives I(s) = (3*(s^2+5*s+2))/(s*(3*s^2+14*s+7))

    Converting I(s) to partial fractions gives I(s)=(1/7)*(3*s+21)/(3*s^2+14*s+7)+6/(7*s)

    From a table in Laplace transforms we find that s/(s^2-a^2)=(sinh(t))/a and s/(s^2-a^2)= cosh(t), so the inverse Laplace gives 6/7+(1/7)*exp(-(7/3)*t)*(cosh((2/3)*t*sqrt(7))+sqrt(7)*sinh((2/3)*t*sqrt(7)))

    Ratch
     
  6. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    kuangmao,

    Enclosed in the attachment is the solution in the time domain in hyperbolic format already given and exponential format. Both are equivalent as proven by the identical plots also shown. You will notice that after a long time the current settles into a steady state value of 6/7 amps, which can be ascertained by an inspection of the schematic. This is also shown on the plots.

    Ratch
     
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