In order to understand electric circuits and how humans can power everything from the lights in their houses to the electric trains (and, more and more over time, electric cars) that take them work, you first must understand what electrical current is and what allows current to flow.

Electrical current is the result of moving electrons, which are near-massless subatomic particles that carry a very, very small negative charge. When you hear of "juice" (as electricity is often called) "flowing" through power wires or your television, this refers to the electron flow through the wires in a circuit. Metal wires are specifically chosen to carry electricity because they have comparatively low ​electrical resistance​.

Electrons are able to serve as a medium for currents because, somewhat like comets orbiting the sun at vast distances, they exist outside the atomic nucleus where protons and neutrons "live" and are considerably less massive than either nuclear particle (and protons and neutrons are awfully light in their own right).

The atoms of different elements differ in mass, number of particles and other inherent ways, and the unique configuration of each atom determines whether it is a good conductor, a poor conductor (i.e., an insulator) or something in between.

Electrical current (represented by ​I​ and measured in ​amperes​ or A) is the flow of ​electric charge​ (denoted by ​q​ and measured in ​coulombs​ or C) in the form of electrons through a conducting medium, such as a copper wire. The electrons move owing to the influence of an ​electrical potential (voltage) difference​ between points along the wire, experiencing ​resistance​ (represented by ​R​ and measured in ​ohms​ or Ω).

• All of this physics is captured neatly by ​Ohm's law​: 

By convention, a positive charge placed near a positive terminal or charge has higher electrical potential than it does at points farther away, all else the same. Voltage has units of joules per coulomb, or J/C, which is energy per charge. This makes sense, because voltage's effect on charges is similar to gravity's effect on masses.

While any point can be chosen as a zero voltage or gravitational potential energy point, a given mass always loses gravitational potential energy as it is moved closer to the Earth's center, and a positive charge always loses electrical potential energy (which can be written ​qE​) as it moves farther from the source positive charge.

Given what you've been presented, you may have already realized that electrons flow in the opposite direction of positive charges, and that they therefore lose electrical potential in the course of flowing as current elements.

This is analogous to a piano falling from the sky and losing gravitational potential energy as it closes in on Earth (energy that is conserved in the form of increasing kinetic energy) and frictional (heat) energy losses owing to air resistance.

As you imagine current increasing in a wire, imagine the number of electrons passing a given point also increasing, with the same applying to current decreases.

• The charge on a single electron is -​1.60 × 10^-19 C​, while that on a proton is +1.60 × 10^-19 C. This means that it takes (1/1.60 × 10^-19) = 6.25 × 10¹⁸ (6 quintillion) protons just to make up 1.0 C of charge.

How easily electrons can move through a material depends on that material's ​conductivity​. Conductivity, usually denoted by σ (the Greek letter sigma), is a property of matter that depends on certain intrinsic characteristics of that matter, some of which were touched on previously.

Most important is the concept of ​free electrons​, or electrons belonging to an atom that are able to freely "roam" far from the nucleus. (Bear in mind that "far" in atomic terms still means an incredibly short distance by normal standards.) The outermost electrons in any atom are called ​valence electrons​, and when there happens to be just one of them, as with copper, the ideal situation for electron "freedom" is established.

Good conductors of electricity allow for current to flow virtually unimpeded, while on the other end of the spectrum, good insulators resist this flow. Most everyday nonmetal materials are good insulators; if they were not, you would continually experience electrical shocks after touching common objects.

How well a particular material conducts depends on its composition and molecular structure. In general, metal wires conduct electricity with relative ease because their outer electrons are less tightly bound to their associated atoms and hence can move more freely. You can identify which materials are metals by consulting a periodic table of elements such as the one in the Resources.

• Concrete, though far less conductive a substance than metals, is nevertheless considered a conductor on balance. This is important given how high a fraction of the world's cities contain concrete!

• Consider the statement "​Most conducting materials have different resistances at different temperatures​." Is this true or false? Explain your answer.

There are more insulative materials than conductive materials in day-to-day life, which makes sense given the strict requirements for insulating materials to merely remove grave levels of danger from everyday processes. Rubber, wood and plastic are both ubiquitous and very useful insulators; practically everyone learns to recognize the characteristic orange tubing around extension cords.

Given the known hazards of mixing electrical appliances and water, it surprises most people to learn that pure water is an insulator. Water that actually consists of hydrogen and oxygen with no impurities is rare, and achievable only by distillation in a lab setting. Everyday water often contains a sufficient number ions (charged molecules) to allow "normal" water to become a de facto conductor.

Insulators, as you would predict, contain materials whose elements have valence electrons bound far more tightly to the nucleus than is the case with metals.

​Resistivity​ is a measure of a material's resistance to the flow of electrons. Measured in ohm-m (Ωm), it is the conceptual opposite and mathematical inverse of conductivity. It is usually denoted by ρ (rho), so ρ = 1/σ. Note that resistivity is different from resistance, which is (or can be) determined by physically manipulating the placement of resistors in a circuit with known resistance values.

Resistivity and resistance in a wire are related by the equation:

where ​R​ and ρ are resistance and resistivity and ​L​ and ​A​ are the length and cross-sectional area of the wire. Insulators have resistivity values on the order of 10¹⁶ Ωm, whereas metals check in in the range of 10^-8Ωm. At room temperature, all materials have some measurable degree of resistance, but the amount of resistance in conductors is small.

• The resistance of most materials is temperature-dependent; often, at cooler temperatures, resistance decreases.

Certain materials achieve a state of 0 resistance at sufficiently low temperatures. These are called ​superconductors​. Unfortunately, achieving the temperatures required for superconductivity – which would result in almost incalculable global energy savings if it could be propagated worldwide into existing technology – are prohibitively low-attainable as of the early 21st century in laboratory settings.