Circuits and YOU!

I'd like to start off by defining electricity and its basic components.

Electricity is the flow of charge that can do useful work. Charge can be either positive or negative. A negative charge exists where there is an excess of electrons, a positive is where we have a deprivation of electrons. Electricity isn't always just the flow of electrons, it can be also considered the flow of ions or other charged sources. This flow of charge is caused by the interaction of charge on the atomic level. Remembering that like charges repel and opposites attract. These attractions and repulsions form the basis for electricity and the movement of charge. Conductors are materials that allow charge to flow freely through it, insulators do not. When we work with circuitry we use conductors to channel the flow of charge through our circuit to do useful work. One unit of charge is the Coulomb(C) which is 6.24 * 10^18 elementary (electron) charges. We also use Q to denote charge.

Charge is going to try and equalize itself when possible and minimize the energy of a system to reach equilibrium. opposite charges are going to cancel each other and like charges are going to spread out so that charge distribution is even throughout a system. This can be demonstrated by having two spheres, with +1Q charge and -1Q charge respectively, touching them and separating them will yield two spheres with 0Q charge on them. Likewise if you were to take two spheres with +3Q and +5Q each and touched them, they would both have +4Q charge each after this interaction.

Two charged spheres separated by a distance r will exert a force on each other. The electrostatic force is the force due to two charged particles and is the product of the magnitude of charge over the square of the distance between them and a constant k. This force is what drives electricity and makes charge want to flow.

Every charged particle has an electric field surrounding it, which propagates out positive and into negative charge. This field is useful in defining the force charged systems have on each other. We can find the electric field of a surface by applying Gauss's law which states that the electric field through an area A is equal to the charge enclosed divided by the permittivity of free space.

With a force, you can do work. Voltage (Electric potential) is the work due to a charge in an electric field and is defined by the dot product of electric field and distance.

Voltage is one of the fundamental components of useful electricity, its a definition that allows us not to worry about the sub atomic interactions of charge and allows us to work on a circuit on the macroscopic scale. Voltage is the work done by an electric field.

Another fundamental component is Current, which is the flow of charge per unit time (Q/t). For a potential (Voltage) to do meaningful work, charge must flow. The unit of current is the Ampere (I) and is the equivalence of 1 Coulomb of charge per Second.

The last meaningful definition is Resistance. If a circuit didn't have resistance the charge would flow from one terminal to another as fast a possible. This will give you an almost infinite current, and your circuit would vaporize. By adding a device that provides resistance, you can control your circuit and measure voltage and current at points in your system and even use them as variables to control you system.

All three fundamental components of electricity come together in Ohm's law which states that the voltage across a circuit is the product of the current through it by the resistance of your circuit.

With this definition you can control every aspect of your circuit.

Another useful definition is Power (Work per unit time) which is defined as

With these two equations you know how to control your system and how much power it is using to operate, the two essential parts to making a useful circuit.

With this basic knowledge in place you'll be able to understand even the most complicated systems.

Formula Sheet.

Formulas are simplified only to demonstrate principle, please look them up if you plan on doing meaningful calculations.

Dot Product =

Electrostatic Force (Coulomb's Law)

Electric Field

Gauss's Law

1 Amp = 1 Coulomb / Second
1 Omh = Resistance of a device with a potential of 1 volt across it and current 1 Amp flowing through it