For practical purposes, I prefer Horowitz & Hill. Griffiths is a bit overkill for circuitry. Slope resistance is a term I hadn’t heard before, but was important in my old job. For most of the diode VI curve it is linear. But, down near the cutoff voltage, there’s a region where the response is nearly square-law. Useful for power measurements.
Back to closer to the op, I guess the electron speed has to go up with voltage because more KE. But because collisions & interactions, & being a closed circuit not an electron gun, electron speed won’t be directly related to energy transfer or any kind of “propagation velocity”. Newton’s cradle might be a better analogy for that.
This is definitely true for instantaneous the quantities: instantaneous power (W) = instantaneous current (A) * instantaneous voltage (V). You have to be careful, though, if the current value is not the instantaneous current, and/or if the voltage value is not the instantaneous voltage, e.g. RMS values.
The ampere (the SI and customary unit of electric current) is explicitly defined as the amount of electric charge passing through a conductor per second. It’s a flow quantity, not a velocity. (For instance, if you get pack more charge into the current stream, you get more charge flow per second at exactly the same flow velocity, just like a completely full pipe carries twice the water current as a half-full pipe at the same water flow speed.)
During my career as an electronics engineer, I was told that current flows from plus to minus then minus to plus, that it was electron flow then hole flow then both but the holes moved faster than the electrons, then that the electrons don’t move through the circuit they just swap positions and then that they don’t move at all they just vibrate faster or slower.
Fortunately the equations didn’t change. Engineering is the science of what electricity does, not what it is.
EEs use the conventional current direction, and assume current is comprised of positive mobile charges. When a battery is powering a circuit, for example, current leaves the battery’s positive terminal and enters the battery’s negative terminal. For a passive element like a resistor, current enters the resistor’s positive terminal and exits the resistor’s negative terminal (where the positive and negative terminals represent the differential voltage across the resistor). As long as you’re consistent with the “rules” for the current directions, everything works out O.K.
Even the equations aren’t “real.” Equations are used to model the circuit. And it’s just that - a model. The equations always approximate, because they don’t take into account higher-order effects. As long as you’re aware that the results won’t be exact, everything is cool.
Actually, resistance of most materials (including nichrome) depends on temperature, and the elements of a toaster are easily hot enough for that to be quite relevant. So an ideal resistor is a pretty poor approximation for a toaster.
In fact, Ohm’s work, what was originally called “Ohm’s law”, was measuring how the resistance of substances changes with temperature (roughly speaking, a material’s resistance is proportional to its absolute temperature).
In the early days of the internet, I had an interesting and humorous discussion with Winfield Hill that started with a usenet post about lemon batteries. I sent him an email asking him what he thought the amp-hour rating was of a typical lemon and it went from there.
The closest is probably a regular ol’ copper wire. It has a pretty low tempco, and thus does a good job of approximating a resistor over a fairly wide range.
Commercial resistors, of course, use alloys that have a very low tempco, and thus do an excellent job of “being” a resistor over a wide temperature range.
Are P and number of electrons and delta time the same in these cases? Why is my lead warming up in case 2 if the number of electrons remains the same? Why is my dc motor running faster in case 1? How does increased potential affect electrons? Do they spin faster?
(Where are all the funny emojis when you need them? I need a better computer!)
Your additional questions require more information. The P here is for the whole circuit U is measured over. Yes it’s the same in both cases. The number of electrons pr time is not the same for both, obviously, you have different current through the two circuits. Is the “lead warming up in case 2” the lead going into the parallel connection? Then it’s warming up because you have twice the current going into it. If you measure the voltage drop over just this lead it will be higher than in case one. Where are you inserting a DC motor in this setup? What’s the voltage drop over just the motor? Increased potential affects electrons by putting more oomph behind them. That means more electrons per second in a wire, or a faster electron in an electron beam.
The water flow analogy works OK for illustration, but the electrons don’t flow like water. They move around locally, encounter resistance and generate heat, but they do not flow. Energy is transmitted by the electromagnetic field outside of the wire.
Consider the case of a transient pulse. A wire of some length is terminated on both ends by resistors equal to it’s characteristic impedance. A voltage is briefly applied to one end of the wire and then removed, for assume 1 microsecond. After a period of time the pulse will appear at the other end of the wire. If electrons flowed then they would displace each other - one electron out for each electron in. And in that case the signal would appear on the output for the entire time the pulse is propagating. But, it does not. The discrete pulse only appears when the electromagnetic field has propagated down the length of the wire.
A larger voltage pulse doesn’t move faster. It just has a larger electromagnetic field.
Oh yeah, if you get the wire cold enough the electrons can’t move at all, so you can propagate electricity without loss.
Not sure what you are trying to say here. If it is superconductivity this isn’t correct.
Electrons are always moving, even in the example of a transient pulse. The idea that the energy is only transmitted in the field outside the wire is a curious and it seems common misunderstanding of an idealised version of propagation. (Shades of a recent discussion about a video on the Veritasium channel on You Tube that got this badly wrong.)
When some conductors are sufficiently cold quantum effects cause the formation of pairs of electrons (Cooper pairs) that behave as composite bosons, which are able to flow feely in the conductor. Far from the cold of a superconductor stopping electrons moving, it is the cold that stops thermal disruption of Copper pairs, allowing the free movement electrons.
As a simple thought experiment. How does a chemical battery work if electrons do not move?
The battery is a voltage source. I’m not a chemist.
As I said the electrons do move. There is excitation due to the presence of the electromagnetic field. But, that is a loss not a propagator.
In a super cooled circuit the electrons do not move, so the electromagnetic field propagates without creating heat - no loss. An LC circuit, once started will resonate for a long time without the addition of energy. It has an infinite or almost infinite Q. How is that possible without electron flow?
How could a pulse propagate using electron flow? Why don’t I see the pulse on the output as soon as I apply it to the input? Can the electrons that are carrying the pulse pass the ones that are not carrying the pulse?