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I know that voltage is the difference in electric potential energy between 2 points and that a higher voltage means more energy for a coloumb of charge (ie a 9V battery means 9 joules per coloumb). But how does increasing the voltage mean more current?

Why does increasing the potential difference mean more current?

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    $\begingroup$ Just FYI, more voltage does not always mean more current. Most conductors obey Ohm's Law, which says that the current along the length of a conductor will be proportional to the voltage between the two ends of it, but when you throw active circuit elements into the mix, other things can happen. For example, there's a component called a tunnel diode which will decrease the current flowing through it as the voltage increases over a certain limited range. $\endgroup$ Aug 10, 2020 at 20:43

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More voltage means the electrons are trying to repel away from each other harder. The harder they try and repel each other, the greater force with which they move which means that they are able to more readily push through obstacles (such as resistance), which means that more of them will push through said obstacles at any given instant in time.

Like pressurizing an air tank. The more air you shove into a tank, the higher the pressure gets which is the same as the force with which the gas trying to spread out to get away from itself. Then if you open the tank to let the air rush out, the airflow is higher when the pressure is higher than when it is lower. Same idea.

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I know that voltage is the difference in electric potential energy between 2 points

Not quite. Voltage is the difference in electrical potential between two points (energy per unit charge).

and that a higher voltage means more energy for a coloumb of charge (ie a 9V battery means 9 joules per coloumb).

Essentially yes. But better to say the higher voltage means that more work is done per unit charge to move the charge between two points.

But how does increasing the voltage mean more current? Why does increasing the potential difference mean more current?

Electric current through a surface is defined as the rate of charge transport across that surface. The greater the rate of charge transport (current) the greater the kinetic energy of the charge. A higher voltage means more work is done per unit charge by the voltage in moving it between the two points, thereby delivering more kinetic energy per unit charge to overcome resistance. That translates to higher current.

Hope this helps.

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Voltage is a kind of "summary" measure of electric field. One way to define it (the electrostatic potential difference, to be specific, since the term "voltage" also has other meanings), is by

$$V_{ab} = \int_a^b\vec{E}\cdot d\vec{\ell}$$

Where $V_{ab}$ is the voltage between points $a$ and $b$, and $d\vec\ell$ is an element of a path between those points.

That means the voltage tells you something about the electric field between those points, without completely defining the electric field at all the points between them (which is why I call it a "summary").

This also means that if the voltage between the two points is higher, it's an indication of stronger electric field in the space between them. And if there's a stronger electric field in a region, then a charged particle in that region will experience stronger forces and tend to accelerate more and move at a higher average velocity, producing a greater current. (But of course these are all just tendencies, exceptions exist, etc.)

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