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Need help with laplace

  1. Jun 3, 2012 #1
    1. The problem statement, all variables and given/known data

    7_12.png

    2. Relevant equations

    For a capacitor: i=C(de/dt)

    3. The attempt at a solution

    Using Kirchhoff's current law at the note above the resistor R2 I get the following equation, which I believe is right:

    C(e0' - ei') + (e0 - ei)/R1 + e0/R2 = 0

    Then, since the source has a constant voltage of A, I set ei' = 0 and ei = A and use Laplace to find the eo(t)

    e0' + e0( 1/(C*R1) + 1/(C*R2) ) = A/(C*R1)

    to facilitate the algebra:

    1/(C*R1) + 1/(C*R2) = ( R1 + R2 )/( C*R1*R2 ) = ε1
    A/( C*R1 ) = ε2

    Then,

    sE0 - E0(0) + (ε1)E0 = (ε2)/s

    => E0(0) = 0

    E0( s + (ε1) ) = (ε2)/s

    using partial fractions:

    E0 = (ε2)/( s( s + (ε1) ) ) = A/s + B/( s+(ε1) )

    A = ε2/ε1 and B = -ε2/ε1

    ε2/ε1 = ( A*R2 )/( R1 + R2 )

    E0 = (ε2/ε1)/s - (ε2/ε1)/( s + ε1 )

    e0 = (ε2/ε1) - (ε2/ε1)e^(-ε1*t)

    e0 = ( A )/( R1 + R2 )*( R2 - R2*ε1*t )

    But I know that the answer to this problem is:

    e0 = ( A )/( R1 + R2 )*( R2 - R1*ε1*t )

    What am I doing wrong? Thanks in advance for any help!
     
  2. jcsd
  3. Jun 3, 2012 #2
    If you want to post in the math section, you should replace variables with x,y,z et cetera, and constants with a,b,c et cetera
     
  4. Jun 3, 2012 #3
    Sorry I am just trying to be consistent with the problem statement. Maybe I posted in the wrong forum (although my question is related to Laplace and not the circuit itself), maybe a moderator can move this to Homework & Coursework Questions > Engineering, Comp Sci, & Technology ?

    Thanks.
     
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