# What makes charges flowing in a circuit with a higher potential difference perform more work?

I understand that a 1.5 V cell will not deliver as much energy per coulomb as a 150 V power supply will.

What I do not understand is that why it is so.

I am digressing now. If we place two point charges at a distance r, then to increase the force between them, we need to increase their charges. This makes sense.

However, if we need to increase the Energy carried by 1 Coulomb of charge in a circuit, we need to increase the potential difference.

Here, the number of electrons remain the same but still, somehow, they are able to do more work.

The definition of electric potential is "electric potential at a point is the amount of electric potential energy that a unitary point charge would have when located at that point"

But why does electric potential energy act upon it at all if there is no charge to attract or repel it?

These seem to be different questions, but they are all linked to a fact that I cannot understand "The same amount of charge performs more work when a higher potential difference is applied"

• Energy=work=Force x velocity. Energy and force are not the same. Even if the forces are the same (which they're not, electrons don't move through a circuit because they repel from a proton or something), the electrons still have higher momentum, so they do more work. Nov 1, 2013 at 13:47
• @RobertMastragostino, Work is not equal to Force x velocity. Work is defined to be the path integral of Force. What you are talking about is the power. Nov 1, 2013 at 14:03

In classical electrostatics and simple circuits, a given potential is always due to a charge (or charge separation). It is just that in many circumstances it is more useful to ignore the details of the charge configuration that leads to the potential (differences) and only worry about the potential itself.

As an example, take a simple battery-resistor circuit; we can calculate the the current just knowing the voltage of the battery and the resistance.

To first order, what is going on inside the battery is that there is a chemical reaction going on that separates charges inside the battery. Thus the two electrodes inside the battery have overall charge densities.

Battery
-  +
-  +
/-----------  +----------\
|          -  +          |
|          -  +          |
|                        |
|                        |
|                        |
\-----------/\/\/--------/
Resitor

(Material inside the battery keeps the charges from jumping the gap, so that charges can only flow through the wires). because of this charge separation, there is a voltage difference between the two leads of the battery.

If everything else were held the same (which might not be possible for real world batteries) then the 150V battery would have $10\times$ as much charge on the two internal electrodes as the 15V battery.