Principles and phenomena of nature:
Fundamental Law of the Universe #1: Material objects are attracted to one another by a gravitational force.
(Newton) Fig 1
Because the earth is such a large and dense object, there is a strong gravitational force between earth and objects close to the earth. Fig. 2
It takes a force that is equal to or greater than the gravitational force to overcome that gravitational force and move objects further apart.
Therefore, force is required to lift an object in a direction away from the earth.
The amount of matter that makes up an object, the total of all its atoms, is called its mass.
It takes a greater force to lift an object with a larger mass (more atoms) than one with a smaller mass. We know this from experience.
In lifting the object we do work. If we lift it one meter we do a certain amount of work. If we lift it two meters, we do twice the work.
Mathematically: Work = Force x Distance Moved
After we have lifted something, it has the potential to do work if it is allowed to fall as the result of being acted on by the gravitational force. For example, if we lifted a rock and dropped it on one end of a see-saw it would cause the object on the other end of the see-saw to be lifted. If we lifted a large bucket of water and let it flow onto a water wheel, the water wheel, connected to some machinery, could grind some grain or move a conveyor belt.
We say that the lifted object has acquired energy which, when released, will do work.
Fundamental particles of matter have charge. Protons are positively charged and electrons are negatively charged. A proton has the same amount of charge as an electron.
Opposite charges attract. Like charges repel.
Oppositely charged particles are attracted to negatively charged particles by an electrostatic force. Like charged particles repel one another by an electrostatic force.
(Coulomb)
To separate opposite charges or to push like charges together requires a force equal to or greater than the electrostatic force.

Charge is not related to or dependent on mass. For example, a proton has 1836 times the mass of an electron but both have the same magnitude of charge. Also, atoms consist of equal numbers of protons and electrons so, ordinarily, have zero net charge. If a molecule consisting of multiple atoms has one extra electron, it has one unit of negative charge. If an atom is missing two electrons, it has two units of positive charge.
The greater the number of unit charges there are, the greater the total charge.
Since opposite charges attract one another, it takes a force to move them further apart.
The further apart we move them, the more work it takes. Also, since like charges repel one another, it takes force to push them together. In pushing them together work is done and they acquire energy which, when released can do work. There is a potential for them to do work so we say they have acquired potential energy.
In a battery there are electrochemical reactions that occur that result in there being an accumulation of positive charges at one electrode of the battery and an accumulation of negative charges at the other electrode. Because the electrochemical reactions that produced the accumulations of charge are not spontaneously reversible, the positive and negative charges don’t move toward one another within the battery.
It takes work to pump molecules of air into a balloon. The accumulation of air molecules in the balloon results in there being an air pressure inside the balloon that is greater than the pressure outside the balloon. That accumulation of air molecules has the potential for doing work. If the balloon nozzle is opened, air molecules flow from a region of high pressure (inside the balloon) to an area of lower pressure (outside the balloon) and can do work such as propel the balloon or turn a fan.
The higher concentration of electric charges in the electrode of a battery is analogous to the higher air pressure inside the balloon. The accumulation of electric charges has the potential for doing work. Because they repel one another, when given the chance, collections of like charges will separate from one another, i.e. move from a region where they are tightly packed to a region where there is fewer of them. When an external circuit is connected to the battery charges can move through the circuit and can do work such as cause a light bulb to light or a CD player to operate.
For the balloon example, the pressure difference is between a region of higher concentration of air molecules to a region of lower concentration of air molecules. For the battery example, we can consider the electrical “pressure” difference to be between a region of high positive charge relative to a region of lower positive charge, or we can consider it to be the difference between a region of high negative charge to a region of low negative charge. Even though in most instances what actually flows in the circuit is negatively charged electrons, the convention is to consider current to consist of positive charges flowing from regions of high positive charge to regions of low positive charge; that is, from the positive terminal of the battery through the circuit to the negative terminal of the battery.

When water flows through a hose, the drops of water that come out of the hose are not the drops that just came out of the faucet. They are the drops that were at the end of the hose. But the water starts coming out of the hose at the same instant that the faucet is turned on. What is it that propels the water out the end of the hose? The water pressure that was just inside the end of the hose. Where did that pressure come from? The pressure that was just a bit closer to the faucet. So there must be a pressure wave that travels more or less instantaneously from faucet to the end of the hose.
What happens if we constrict the hose? The flow of water from the hose decreases. We have increased the resistance to flow. It is harder for water to flow through a smaller cross section area. Even though the water pressure at the faucet is the same, there is less water flowing. The amount of water that flows through a cross section of hose per second is the water current. If there is no place along the hose for the water to accumulate or to escape, then the amount of water passing through any cross section of the hose must be the same. Notice we have said nothing about how fast drops of water are moving, only how many have passed through a cross section per second.
Similarly, if we put a resistor in an electrical circuit, the flow of charged particles will be decreased. Fewer charged particles will pass through a cross-section of a wire that did without the resistor, even though the battery voltage is the same.
The water coming from the faucet has a certain pressure resulting from work done at the water company to pack water drops in the pipe. It therefore has a certain potential energy.
Since it takes work to make the water go through the constriction in the hose, some of that potential energy is used. There is less potential energy, and therefore less pressure, at the other end of the constriction. There is a pressure difference between the faucet side of the constriction and the other side of the constriction.
Similarly,