Engineering Mathematics help

[yasir_ali86]

Hey Guys,
I have some questions regarding Math use in Electronics, which some one asked me and i was somewhat unable to answer them. but i want to know the answers of the Questions. the Questions are:

1- How first order and second order defferential equations are helpful in the process of analysis of Electrical Networks?

2-What is the role of initial Condition of Electrical circuits in defferential equations?

3- In what situation Laplace Transform is required?

Thanks

 

[Kral]

yasir_ali86,
A complete answer to your question would be rather lengthy, but here are some examples of situations where differential equations are useful or necessary:
1
The fundamental relationship between current and voltage in a capacitor involves a first order derivative: I = Cdv/dt.
.
The fundamental relationship between current and voltage in an inductor involves a first order derivative: V = Ldi/dt.
.
The solution to the response of many filter circuits involves a 2nd order or higher differential equation.

2
Example: You want to find the response of a simple RC lag filter to a step input. The voltage vs time curve depends on whether the voltage to which the capacitor was initially charged affects the output.

3
You need the response to an electrical circuit (a filter, for example) that is described by a differential equation. The use of Laplace transforms reduces the solution to a simple algebra problem. Furthermore, initial conditions are included in the LaPlace transform of the system and its input, so you don't have to handle them separately.

The book "Laplace Transforms aand Control Systems for Technology has answers to all your questions. I believe that it is currently out of print, but is available used for a reasonable price. Amazon has one for sale for $0.46 (yes, that's 46 cents US)
Regards,
Kral

 

[ark5230]

Kral's information is perfect and complete.
Regarding point 3, the drifferential equations can be solved by any convenient method like analytical or numerical method. In such a case the Laplace transform does not come into picture and you are done with the problem.
However there are situations where you happen to need analytical solution and conventional methods of solving differential equations pose problems or are too lengthy, in such cases the Laplace transform many times provide a easier way of solving such equations.

 

[Electronica]

use Ervin Keyzig book

 

[raghuram_msc]

HI....

Laplace transform is a convenient way to solve a differential equation(s) only when they satisfy dirichlet's conditions....

Wherever they dont, alternative methods like numerical solutions are taken recourse to..!!

Hope this helps..:idea:

-Sai

 

[mishra.sanjeev2008]

You can solve network theory with Laplace Transform

 

[yasir_ali86]

Hey! Can some one link me to any website or name a book that explains and shows an example that how they are being use in the Electrical Networks.


Thanks

 

[DigitalLogician]

"Electromagnetic Compatibility Handbook" by Dr. Kaiser is superb.
An additional note: all feedback electronics are essentially differential equations. This means, robotics, the air conditioning system in your house, etc.

Also, in real life the interactions between electric field, particle, and magnetic field are all defined by differential equations.