On Jul 7, 9:36*pm, joe wrote:
Keith Dysart wrote:
On Jul 7, 8:05 am, joe wrote:
Keith Dysart wrote:

current law derives from conservation of charge.

Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.
Conservation of charge requires that:
* the charge added to a region
* - the charge removed from a region
* equals
* the charge originally in the region
* + the increase of charge stored in the region
When the charge can be described with functions of time, we can write:
* Qin(t) - Qout(t) = Qoriginal + Qstored(t)
Differentiating we obtain
* *Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt
At a junction, where charge can not be stored, this reduces to
* *Qin(t)/dt - Qout(t)/dt = 0
Alternatively
* *Qin(t)/dt = Qout(t)/dt
Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.
I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be
* *EnergyIn(t)/dt = EnergyOut(t)/dt
And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.
Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain
* *PowerIn(t) = PowerOut(t) * *(at a junction)
But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.
I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.
...Keith
How do you define energy of a node without reference to another node.
How is it measured

I am sorry, I do not understand the question. Can you provide a bit
more context, or perhaps a representative example?

...Keith

Sure. You described charge flow in and out of an isolated node with no
need to reference any other node or part of the circuit. Then you say
the same thing can be defined for energy. However, how is energy defined
in terms that only refer to characteristics of the node without
involving any other part of the circuit or other nodes.

Perhaps some examples will help.

Consider the output terminals of a generator to be junction. Then the
power delivered from the generator to the junction must exactly equal,
at all times, the power taken from the junction by the load, since
there is no storage in the junction.

It should be noted that the 'junctions' used for a power analysis
are not the same as the junctions used in Kirchoff's current
law. The concepts are analogous, not identical.

Another example. In the simple Thevenin generator, the power provided
by the voltage source must exactly equal, at all times, the power
taken by the resistor plus the power taken by the load. In this
example, it is difficult (impossible?) to identify a physical
'junction' where the power must balance, yet the notion is still
applicable.

....Keith