learning circuit theory
So i am mainly learning about kirchoffs law and analysing combinations of resistors and possibly other components, which cannot be analysed by ohms law alone. However i have a number of questions which hinder my understanding that id like to post and hopefully gain some answers.
We have a voltage law and a current law which states respectively that:
sum of pd around any closed loop is 0.
current into any node = current leaving that node or equivalently the current into any node is 0 where a plus or minus sign is used to denote the direction of current wrt that node.
First i will ask where these laws come from and what they really mean?
Sum of pd around a loop equals zero comes from the property of electric fields generated by static charges. To be technical, the static electric field is a conservative field, which means that if you move a test charge around from A to B the energy gained/lost does not depend on the route you take. From this comes the concept of potential. If you go around a loop then when you come back to the starting position the net energy change is zero, so the voltage change is zero. Mathematically, it comes from Maxwell's equations give the static E field from a Div only. (Magnetism is different as it based on Curl, like a changing electric field).
Sum of current into a node equals zero comes from conservation of electric charge.
They come from Maxwell, James Clerk.
He looked at a load of existing knowledge about electricity and magnetism and consolidated it into 4 basic equations, these otherwise known as Ampere's Circuital Law (which he elaborated), Gauss's Law, Gauss's Law for magnetism and Faraday's Law. These describe the behaviour of electric and magnetic fields and electric charge and current in space. You can look them up in Wikipedia, but the compact mathematical expressions you will find using the curl and divergence operators require practise to manipulate. They can be broken down to some simplifications and special cases such as Ohm's (or Kirchoffs) Law.
What they really mean is a great deal. They don't account for mass or gravity so they don't explain everything, but they're a fundamental description of some aspects of matter and space and they permit the understanding and prediction of the behaviour (such as the speed of light) of electromagnetic (radio) waves, which was the main impact of his work and without which Einstein's later work on relativity would have been impossible.
It's normal to work up to a consolidated understanding of the subject by studying the simplifications and developing mathematical skills from the ground up, starting with algebra and progressing through calculus and vector analysis.
Other than that, they come from observations.
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