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I am in secondary school in the UK, and at this point in physics the information we are given is very vague at a fundamental level. My main concern is with electricity and circuits, and the measures involved: current, potential difference, charge and resistance, and specifically I want to know exactly what they are measures of.

From the equation sheets that we are given, and a bit of intuition, I can get some of the way. Firstly, I know that electrons have a constant charge of -1, so I would assume that charge is a measure of the amount of electrons. We are given that $I={Q\over t}$, so I can see that current is a measure of charge in a given time, or essentially the number of electrons that flow through in a given time (I guess the flow rate of electrons).

Then, we are told that $P=IV$, and $P={E\over t}$, so I can work out that $E=tIV=QV$ so $V={E\over Q}$. This appears to me to mean that potential difference is a measure of the amount of energy in each electron, but given the measure's name and how a voltmeter is used I think it is actually the amount that this energy per electron changes through components, or the difference between one end and the other.

Finally, there is resistance, given by $R={V\over I}$. To me, resistance means the amount that a wire resists against electrons passing, but its measure seems to be the change in energy per electron per flow rate of electrons, and in my mind this makes little sense.

The method of calculating resistance seems to make sense - if there is large resistance against electrons, then the current will be small, and low resistance allows more electrons to flow through, so the current is big (hence inverse proportionality between them). I think I understand the potential difference part - if resistance is small, then electrons collide with less atoms, so less energy is lost, so potential difference is low. If resistance is large, electrons are colliding with more atoms, so more energy is lost, so potential difference is large (hence direct proportionality).

The only part I don't understand is precisely what 'change in energy per electron per flow rate of electrons' means, because there's too much division for me to make much sense of it. Also, I would like to know if the way I am thinking of these measures is correct, because although it all seems to make sense in my mind, this is just what I have worked out from equations I have been given.

Finally, I know that my terminology is not very scientific, its just what lets me make sense of it.

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  • $\begingroup$ "change in energy per electron" is a meaningless sentence. You can see that when the difference in potential between two points changes, the resistance needs to change in order to let the flow rate stay the same right? $\endgroup$ – Feyre May 12 '16 at 15:32
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The information you are given was actually vague at a mathematical level, but with your resources you have you already have a mostly correct grasp of the physical quantities.

The most important variables in a circuit are voltage ($V$) and current ($I$), because you can measure them unlike the charge.

As you already stated $I = \frac{Q}{t}$, and its a measure of how many charges (electrons) move through the circuit per unit of time, is the electric analog of speed ($\vec v = \frac{d}{t} \rightarrow$ How many meters the object is moving per unit of time)

The potential $V$ is slightly harder to grasp, it's a measure of how much kinetic energy a charge would gain if it could travel through the circuit undisturbed.

In a more clasical picture, think of a ball held at a given distance from the ground, if you release the ball it would hit the ground at a certain speed, and if you hold it even higher the speed will be greater (thus have more potential) Please be aware that the potential does not have any information of the charge/particle (so for a ball held off the ground, its potential energy is $U = mgh$, thus the potential is $V = gh$) This distinction is not critical, but is better if you don't mix the concepts incorrectly.

To finish with voltage, you can think of the voltage source as a huge tank above the ground (The higher, the more potential energy) with many balls in it, so when you let the balls pass, they will start hitting the ground.

With this picture is easy to make sense of the energy and the power output. The Energy stored, would be all the balls held at height by the tank, which means that the energy stored would be $E = Q*V$, now we can't really measure the total numbers of balls in the tank (they are a huge number), but we can measure the current (or number of balls per unit of time) that leaves the tank, hence we have the power as the energy that leaves the tank per unit of time $P = \frac{E}{t} = I*V$ Since we can measure the Voltage and current easily we can measure the power output with simple multiplication, and we can indirectly measure the total energy by waiting until the "tank" runs out of energy with the constan measure of the power $E=T*P$ (Here T is a large time, say 10 hours, compared to the current measured by the second)

Your physical picture of the resistance is quite accurate, but keeping this picture will help you make better sense of it. You can think of the resistence as a "trafic jam", no matter how many cars you want to allow to pass, only so many can pass per unit of time. Similarly, in our Tank with balls analogy, you can think of an elementary resistence as a sort of net for which traps the balls, so if a ball hits the mesh, it will bounce a little and fall over the net again, but if it doesn't then it will just fall off. A single net would barely have any balls hitting it, but a large array will have many balls hitting one or another. A resistence would be several nets at small distance so to pass through the nets the balls would bounce quite a few times.

We know the potential at which the balls hit the net, and we know the amount of balls per unit of time at which the balls hit the ground, so we can estimate the number of nets by dividing these 2 quantities, which would give us the measure of the resistence hence $R = V/I $ or $V = R*I$ as the measure of the lost of potential energy through the nets

I hope this clarifies your confusion

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