Circuit analysis by local application of Kirchhoff's current law and Ohm's law

Question

First of all I want to say that this is a new field for me, so please excuse any inaccuracy in the used terminology and the lack of understanding of some concepts.

I am trying to understand whether it is possible to perform a circuit analysis (find voltage and current around complex circuit) by applying the following constraints:

• Apply Kirchhoff's current law for every junction
• Ohm's law for all electrical components
• For each energy source one terminal has a predefined V, while for the other the V is 0

I have found a description of the method for Nodal Voltage Analysis which seems not to need to enumerate all closed circuits and apply Kirchhoffs's voltage law.

In the end, I want to be able to perform such circuit analysis by applying the above defined "local rules" which do not rely on knowing of the whole network. So it is an algorithm which relies on the assumption that "the whole = the sum of the parts". What do you think, is such an approach possible?

Answer 1

There are several problems with the approach you describe.

If there is a voltage source connected to a node, then you can not directly write an expression for the current through that source. In other words, it introduces an unknown current. There are ways to deal with this but they require considering more than one node at a time.

Ohm's Law applies only to ideal resistors. It does not apply to any other kind of component.

You can't arbitrarily assign a value for the voltage across an energy source that is an ideal current source.

Each node in the circuit must have its own voltage. If you go around assigning 0 voltage to different nodes it will be very difficult to form a set of consistent equations.

So the bottom line answer is no, you can not, in general, solve a circuit analysis by analyzing one node at a time. You must create a set of independent simultaneous linear equations and then solve that set of equations.

There is an approach that relies on linearity and uses something like "the whole is the sum of the parts". The technique is called superposition, and it is much different from what you describe.