# RL circuit transient response

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

1. ### stupid Thread Starter Active Member

Oct 18, 2009
81
0
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
5,448
782
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
5,448
782
Hi s,

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

My attachment is pdf of a solution

rgds,

t_n_k

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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.

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)