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
Hi there,
I'd like to add a little here too...
First and second order differential equations in particular are easier to solve than the higher order ones so these are used not only to solve circuits that involve one or two energy storage elements but also to help get a grasp of how higher order circuits work because they are so much simpler.
It's a good idea to study these two first and understand the role of some of the variables clearly before moving on to higher order circuits.
Initial conditions in an electrical circuit can be looked at as the initial values that the energy storage elements have before the analysis begins in time. For example, a capacitor may have zero volts or it could have a hundred volts already stored in it before the analysis starts.
Initial conditions help to solve for unknown constants too...knowing what the initial conditions are often help solve for the unknown constant after integration.
It should be noted however that the initial conditions are not always exactly the initial conditions of the energy storage elements themselves, but many times they are.
Laplace Transforms can be used for any circuit involving resistors, capacitors, and inductors with sources also. The Laplace simply transforms the mathematical expression from the time domain to the frequency domain where many times things are easier to work with, and the Inverse Laplace takes it back into the time domain. Laplace Transforms make things easier sometimes.
Laplace Transforms are not particular suited to multivariate solutions however because often finding the inverse requires factoring the denominator, which can be impossible in multivariate situations in higher order systems.
In addition to those studies, it's also a very good idea to look into numerical methods for solving differential equations as these turn out to be very useful sometimes and very interesting too.