Electric charge: What automatic reaction does that phrase produce when you read it? A tingling sense, perhaps, or the image of a bolt of lighting splitting the sky? The colorful display of flashing lights in a city like Paris or Las Vegas? Perhaps even an insect that somehow glows in the dark as it wends its way across your campsite?

Until recent centuries, not only did scientists have no way to measure the speed of light, they had no idea what physical phenomena underlie what's now known as "electricity" in the first place. In the 1800s, physicists first gained an understanding of the tiny particles involved in current flow (free electrons) as well the nature of the forces compelling them to move. It was clear that electricity could do considerable good if it could be safely "made" or "captured" and the electrical energy used to do work.

Electric charge flow occurs readily in substances classified as ​conductive materials​, while it is impeded in those known as ​insulators​. In a metal wire such as a copper wire, for example, it is possible to create a ​potential difference​ across the ends of the wire, causing a flow of charge and creating a current.

​Electric current​ is the average rate of flow of electric charge (i.e., charge per unit time) past a point in space. This charge is carried by ​electrons​ moving through a wire in an electric circuit. The higher the number of electrons moving past this point per second, the greater the magnitude of the current.

The SI unit of current is the ampere (A), often informally called "amps." Electric charge itself is measured in coulombs (C).

• The charge on a single electron is -1.60 × 10^-19 C, while that on a ​proton​ is equal in magnitude but ​positive​ in sign. This number is considered the ​fundamental charge​ ​e​. The base unit of the ampere is therefore coulombs per second (C/s).

By convention, ​electric current flows in the opposite direction of the flow of electrons​. This is because the direction of current was described before scientists knew which charge carriers were the ones that were moving under the influence of an electric field. For all practical purposes, positive charges moving in the positive direction offer the same physical (computational) result as negative charges moving in the negative direction when it comes to electrical current.

Electrons move toward a positive terminal in an electric circuit. The electron flow, or moving charge, is therefore away from the negative terminal. The movement of electrons in a copper wire or other conductive material also generates a ​magnetic field​ that has a direction and magnitude determined by the electric current direction and hence the movement of electrons; this is the principle upon which an ​electromagnet​ is built.

For the basic conventional current scenario of a charge moving through a wire, the formula for current is given by:

where ​n​ is the number of charges per cubic meter (m³), ​e​ is the fundamental charge, ​A​ is the cross-sectional area of the wire, and ​​v_d​​ is the ​drift velocity​.

Although current has both a magnitude and a direction, it is a scalar quantity, not a vector quantity, as it does not obey the laws of vector addition.

​Ohm's law​ gives a formula for determining the current that will flow through a conductor:

where ​V​ is the ​voltage​, or ​electrical potential difference​, measured in volts, and ​R​ is the electrical ​resistance​ to the current flow, measured in ​ohms​ (Ω).

Think of voltage as a "pulling force" (though this "electromotive force" is not literally a force) specific to electrical charges. When opposite charges are separated, they are attracted to one another in a way that diminishes with increasing distance between them. It is loosely analogous to gravitational potential energy in classical mechanics; gravity "wants" high things to fall to Earth, and voltage "wants" separated (opposite) charges to come crashing together.

Volts are equivalent to joules per coulomb, or J/C. They thus have units of energy per unit charge. Current times voltage thus gives units of (C/s)(J/C) = (J/s), which translate to units of (in this case electrical) power:

Combining this with Ohm's law gives rise to other useful mathematical relationships involving the flow of current: P = I²R and P = V²/R. These show, among other things, that at a fixed level of current, power is proportional to resistance, whereas if voltage is fixed, power is ​inversely​ proportional to resistance.

While moving charges (current) induce a magnetic field, a magnetic field can itself induce voltage in a wire.

• ​Direct Current (DC):​ This occurs when all electrons flow continuously in the same direction. This is the type of current in a circuit connected to a standard battery. Batteries, of course, can and do supply only a vanishingly small amount of the energy required to power human civilization, though ever-improving technology in the area of solar cells is offering the promise of better potential for energy storage.
• ​Alternating Current (AC):​ Here, electrons oscillate back and forth ("wiggle," in a sense) very rapidly. This type of current is often easier to generate in a power plant, and it also results in less energy loss over a large distance, which is why it is the standard used today. Every light bulb and other electrical appliance in a standard early 21st-century home is powered by AC.

With AC, the voltage is varied in a sinusoidal way, and is given at any time ​t​ by the expression V = V₀sin (2πft), where ​V₀​ is the initial voltage and ​f​ is the frequency, or number of complete cycles of voltage (maximum to minimum back to maximum value) in each second.

An ammeter is a device that is used to measure current by connecting it in series – and never in parallel – in an electrical circuit. (A parallel circuit has multiple wires between junctions – in other words, at the power source, capacitors and resistors – in the circuit.) It operates on the principle that current is the same through all parts of a wire between two junctions.

An ammeter has a known, low intrinsic resistance and is set up to give a ​full-scale deflection​ (FSD) at a given current level, often 0.015 A or 15 mA. If you know the voltage and manipulate the resistance using the ammeter's shunt resistance function, you can determine the current; you know what the value of the current flow ​should​ be using Ohm's law.

1. Calculate the drift velocity of electrons in a cylindrical copper wire with a radius of 1 mm, or 0.001 m) carrying a 15-A current, given that for copper, n = 8.342 × 10²⁸ e/m³.

The area ​A​ of the cross-section of the wire is πr², or π(0.001)² = 3.14 10^-6 m².

• The negative sign indicates that the direction is against that of current flow, as expected for electrons.

2. Find the current I in a 120-V circuit that has 2-Ω, 4-Ω and 6-Ω resistors in series.

Resistors in series are simply additive (in parallel circuits, the sum of the total resistance is the sum of the reciprocals of the individual resistance values). Thus:

3. A circuit has a total resistance of 15 Ω and a current flow of 20 A. What are the power and voltage in this circuit?