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.