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## Why is there close to zero potential difference in conductors in a circuit?

 Quote by glenn21 Yeah, I see what your talking about, it just doesn't make sense to me that no energy is converted through conductive sections.
That is true for idealized circuit diagrams, but (other than super conductors), there is some energy converted to heat even in a conductor.

 Quote by glenn21 In what way is a circuit different than if a wire was short circuited between the capacitor terminals? Would the EPE then still be related to position between the plates?
I mentioned this case before. All of the energy would be converted to heat (and light if glowing) in the wire (ignoring issues like a battery where there is internal resistance, or the equivalent in terms of the rate of conversion of potential chemical energy into electrical energy and heat). In this case, the EPE would be relative to position in the wire, assuming uniform resistance.

You also need to keep in mind that for a given potential (voltage), the higher the resistance of the total circuit, the lower the current and the lower the amount of energy converted into heat. So if there is a high resistance component in a circuit that is otherwise all conductor, almost all of the conversion of energy to heat takes place in the resistor, but the power (rate of energy conversion) is much less because of that resistor.

 Isn't all of this overcomplicating things? The original question was "Why is there close to zero potential difference in conductors in a circuit?" The answer to this is that conductors have close to zero resistance. For instance a typical 1mm2 stranded wire has resistivity of c.0.0175Ω/m. Carrying a current of 1A the PD along 1m of wire is therefore 0.0175V, and the heat loss along the wire is a negligible 0.0175W. Low resistivity is the definition of a conductor so you can't really ask 'why does a conductor have low resistivity', but it does make sense to ask 'what are the characteristics of a conductor that make it have low resistivity'. The answer is that electrons can move freely along the conductor. Considering your falling ball analogy, a conductor is a bit like a dust storm - the ball is impeded slightly by the dust, but not enough to notice. A resistive component however is a bit like the 'cloud of rocks' - the ball collides with the rocks and transfers most of its kinetic energy to them. However it is very important to realise that electrical energy is not the kinetic energy of electrons (which is tiny by comparison), any more than the energy equivalent of a rest mass given by E=mc2 is the kinetic energy of a falling ball.
 Recognitions: Gold Member Science Advisor But the Kinetic Energy analogy is not appropriate. There is so little, compared with the total energy transferred that it just doesn't count. It's like saying the kinetic energy of your bicycle chain is what gets energy from your feet to the wheel. If there is any mechanical analogy it's that of Work (force times distance) which corresponds to Charge times PD. But I agree that, too many times, people seem to demand an over-familiar (and often metaphor-laden and circular) treatment of new concepts rather than accept and use them. After a very short while, with the latter approach, what was unfamiliar and difficult becomes familiar and reasonable. Remember, everything was unfamiliar once - we weren't born with any of this knowledge.

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 Quote by rcgldr You also need to keep in mind that for a given potential (voltage), the higher the resistance of the total circuit, the lower the current and the lower the amount of energy converted into heat. So if there is a high resistance component in a circuit that is otherwise all conductor, almost all of the conversion of energy to heat takes place in the resistor, but the power (rate of energy conversion) is much less because of that resistor.
That should have been: ... the higher the resistance of the total circuit, the lower the current and the lower the rate of energy converted into heat.

 Thanks so much for all your help. I think I know what my conceptual difficulty was, it struck me when sophiecentaur said, why should it be transformed? I am so use to textbook physics examples where for example you have an inclined plane, he has a certain GPE at the top - what is his KE at the bottom. But in the case of circuits, there is very little conversion to KE, it doesn't have to be converted to forms of energy either, the energy is literally stored relative to what the upcoming resistance is in the circuit as rcgldr said. I just got lost in the maths, the formula suggests it must decrease with distance, but that relies on energy conversion, but if you think of what potential energy actually is,stored energy, it makes perfect sense that it isn't always converted. I managed to think up something that is analogous to this, and that is a hydro system whereby water falls off a cliff and on the way down spins a turbine then exits down back to the river and a lift of some sort lifts the water back up to the cliff. In this example again there isn't too much converted to EK, each water particle needs to store most of it's energy to be able to pass through the turbine, and so it's GPE is almost constant before it and close to zero after it. Thank you all so much for your time and patience, I understand now, it's just a new way of thinking which I never really thought of.