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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? |
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