The Fundamentals of Electricity
Electric charge (conventionally denoted Q) is a property of matter that describes the force experienced (and exerted) in the presence of other electrically charged matter. An electrically charged particle will therefore perform work on another electrically charged particle, which is an example of energy by definition. Electricity is defined as the collection of phenomena associated with the presence of electrically charged particles. These particles can either be static, representing an accumulation of charge, or flowing as an electric current.
There are two types of electric charge: positive and negative. Alike charges will repel one another, and opposite charges will attract. For the most part we deal with protons and electrons as the fundamental charged particles, and each carries an "elementary charge," which describes its magnitude. In other words, protons carry one positive elementary charge (denoted +1 e), while electrons carry -1 e.
Although the elementary charge is a unit unto itself, in the context of energy and electricity it is often impractically small. In fact, while all charge is composed of individual charged particles carrying 1 (or -1) e, it is often more convenient to think of charge in terms of the force exerted by its movement or by its potential when static. When discussing electricity, the Coulomb (C) is the preferred unit of measurement. One Coulomb is roughly equal to 6.241 x 1018 e.
As previously touched on, a particle or material with a net positive charge will repel another positively charged material and attract one with a negative charge. In other words, electrically charged materials exert force on other electrically charged materials. For instance, if you were to take a proton and physically separate it from an electron, there would be a force of attraction between them. If allowed to move freely, these two oppositely charged particles would recombine, transforming the potential energy that existed between them due to their attraction into the kinetic energy of their motion toward one another. This is analogous to the transformation of gravitational potential energy into kinetic energy when an object is dropped from some distance above the ground. In this case, rather than gravitational potential energy created by the distance of the object above the ground, we have electric potential energy, created by the separation of two oppositely charged materials.
Voltage (denoted V), sometimes referred to as "electrical potential difference" or "electro-motive force" is the difference in the electrical potential energy per unit of charge between two positions in space. It tells us the amount of energy (again per unit of charge) that is required to separate two charged materials some distance. To give an example, if it requires 9 Joules (J) of energy to separate 3 Coulombs (C) of electrical charge, the resulting electrical potential difference (which is to say voltage) would be 3 Volts (V). Accordingly, the equation for voltage is:
V = W/Q
W: Energy (or Work)
By the same token, voltage is also the amount of electrical potential energy per unit of charge contained by the charges once they have been separated. Therefore, if 3 C of charge travels across the 3 V of electrical potential difference, that represents 9 J of electrical kinetic energy available to do work on some other system. This decrease in voltage as charge moves from a position of higher electrical potential energy to a position of lower electrical potential energy is referred to as a "voltage drop."
Voltage is also (synonymously) the motive force that drives the movement of charge across the electrical potential difference. Gravity is once again an apt - if somewhat imperfect - analogy here. The force of gravity causes both the difference in potential energy of a mass as it is raised above the Earth and the motion of the object once it's released.
Current (denoted I) is the rate at which charge is flowing. It is defined as the amount of charge that passes a point in a second. For example, if 3 Coulombs of charge pass a single point in a wire over the course of 2 seconds, there exists a current of 1.5 Amperes (A) in the system.
I = Q/t
The relationship between current and voltage is integral in understanding how much power is "developed" in a system, that is to say, how much electrical power is generated and dissipated. It is important to understand that in a circuit, current is a conserved quantity. At each junction in the circuit, the sum of the current entering a node must be equal to the sum of the current leaving it. Therefore, in a circuit with one single loop, the current would be the same across each electrical element. Current doesn't "drop" in the same way that voltage does, but in fact remains constant.
Resistance is the opposition to electrical current in a material. To put it another way, resistance is the inverse of a material's ability to conduct electricity. Resistance is an important concept to understand when discussing electricity because it dictates how quickly charge will flow through a circuit and therefore how much current will exist.
Ohm's Law gives us the mathematical relationship between voltage, current and resistance and is one of the most fundamental tenants in understanding electricity:
V = IR