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

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
790
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
11,946
2,561
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.

5. t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Hi s,

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

My attachment is pdf of a solution

rgds,

t_n_k

File size:
35.5 KB
Views:
37
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
790
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)