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what happens to reflected energy ?
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 |
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