RL circuit transient response

Discussion in 'Homework Help' started by stupid, Nov 9, 2009.

  1. stupid

    Thread Starter Active Member

    Oct 18, 2009
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    i m at a loss to how the answer is arrived.

    iL= -(R/L)∫(iL-(E/R))dt, where limit is i(t) & Io

    the answer provided is,
    i(t)=e^(t/τ)(I_{o}-(E/R)) + E/R

    i m stuck, pls help

    thanks & regards,
    stupid
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Differentiate the equation in iL with respect to time (both sides) and solve the resulting differential equation.
     
  3. stupid

    Thread Starter Active Member

    Oct 18, 2009
    81
    0
    hi tnk,
    there is no t element with either iL & E/R
    how can i proceed?

    i thought it should be integration instead of differntiation?

    regards,
    stupid
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,152
    1,794
    That current and voltage depend on t is implicit. If they did not there would be no need for differential equations since nothing would ever change. In cases like this you can expnad the short hand as follows:

    i -> i(t) ; i(t) is a function of t, but we do not yet know the form of this function

    The derivative of i(t) is just d/dt[ i(t) ], and since we don't know the form of i(t) we cannot know the form of di/dt. However, the differential equation puts a severe restriction of the form of i(t) and therefore di/dt. Once you see the form of a differential equation you can make an ansatz

    http://en.wikipedia.org/wiki/Ansatz

    and the solution falls right out.

    Does that help you out a bit?
     
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Hi s,

    Can't bring myself to call you stupid - seems not polite.

    My attachment is pdf of a solution

    rgds,

    t_n_k
     
  6. stupid

    Thread Starter Active Member

    Oct 18, 2009
    81
    0
    thank u tnk.
    i need to digest & reflect upon my weakness.

    do expect i may come back with questions related to that.:D

    regards,
    stupid

     
  7. stupid

    Thread Starter Active Member

    Oct 18, 2009
    81
    0
    i m trying another way, say

    given iL= -(R/L)∫(iL-(E/R))dt

    diL/(iL-(E/R))= -(R/L)dt

    iL/(iL-(E/R))= ∫-(R/L)dt -----eq1

    (i have a feeling the above eq may b wrong.)

    however we know say y=2x^{2}
    dy/dx = 4x

    dy= 4x. dx
    y= ∫4x.dx

    given that logic i cant reprove eq1, can i?

    regards,
    stupid




     
  8. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    No - You can't do that.

    Essentially, you've re-arranged things in the same manner as I did before making the change of variable substitution [z(t)=iL(t)-(E/R)] - which I did to allow me to more easily perform the integration of both sides.

    Remember ∫(1/x)dx=ln(x)
     
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