RL circuit transient response

Thread Starter

stupid

Joined Oct 18, 2009
81
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
 

t_n_k

Joined Mar 6, 2009
5,455
Differentiate the equation in iL with respect to time (both sides) and solve the resulting differential equation.
 

Thread Starter

stupid

Joined Oct 18, 2009
81
Differentiate the equation in iL with respect to time (both sides) and solve the resulting differential equation.
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
 

Papabravo

Joined Feb 24, 2006
21,094
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?
 

Thread Starter

stupid

Joined Oct 18, 2009
81
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

Hi s,

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

My attachment is pdf of a solution

rgds,

t_n_k
 

Thread Starter

stupid

Joined Oct 18, 2009
81
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




Hi s,

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

My attachment is pdf of a solution

rgds,

t_n_k
 

t_n_k

Joined Mar 6, 2009
5,455
iL/(iL-(E/R))= ∫-(R/L)dt -----eq1

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