- #1
Bipolarity
- 776
- 2
Let's say I have a circuit consisting only of a finite number of batteries and resistors, all ideal. Given an arbitrary shape of this circuit, will I always be able to "solve" this circuit, i.e. find the missing variables (current through any wire, voltage across any two points) by using the Kirchhoff's laws in conjunction with Ohm's laws?
If yes, can this be proven mathematically? Where would I find a proof? Surely it involves proving that a certain coefficient matrix of some linear system is invertible? Perhaps it will require some graph theory?
If not, under what conditions can the circuit be solved for?
What about when we add dependent components to the circuit?
One thing I noticed is that if you have a circuit with N nodes and write out equations for all nodes, 1 of the equations will be linearly dependent on the other (n-1) equations.
I am reading my introductory circuits text, but have a good linear algebra background, so I like to see a very rigorous justification of the methods employed by my text.
Thanks!
BiP
If yes, can this be proven mathematically? Where would I find a proof? Surely it involves proving that a certain coefficient matrix of some linear system is invertible? Perhaps it will require some graph theory?
If not, under what conditions can the circuit be solved for?
What about when we add dependent components to the circuit?
One thing I noticed is that if you have a circuit with N nodes and write out equations for all nodes, 1 of the equations will be linearly dependent on the other (n-1) equations.
I am reading my introductory circuits text, but have a good linear algebra background, so I like to see a very rigorous justification of the methods employed by my text.
Thanks!
BiP