Electric charge is a fundamental property of certain subatomic, elementary particles of matter.  The amount of charge determines the strength of the particle's coupling to electromagnetic (EM) fields.

Likewise, the amount of mass determines the strength of a particle's coupling to gravitational fields.  Every particle with a mass is the source of a gravitational field and every particle with a charge is the source of an EM field.

However, unlike mass, charge is polar—having either positive or negative values.  So, while the gravitational force is always attractive, EM forces can be either attractive or repulsive.

Electrons and Protons

Two of the elementary particles that possess electric charge are electrons and quarks.

The amount of charge held by an electron is called one negative elementary charge ( symbol −e) .  This amount of charge is a fundamental physical constant.

The proton is a composite particle containing 3 fractionally-charged elementary particles called quarks.  Two of the quarks have a charge of +2⁄3 e and one has a charge of −1⁄3 e.  So, all combined, the 3 quarks give the proton one positive elementary charge ( symbol +e or just e).

●  The math symbol for electric charge is  ‘q’  or  ‘Q’, from the 18th century phrase “quantity of electricity”.

●  The unit of electric charge is the coulomb, abbreviated ‘ C ’ — capital C because Coulomb was a person.

How Many Electrons
are in a Coulomb?

Around 1910, Robert Millikan became the first person to experimentally obtain a value, in coulombs, for the tiny elementary charge of the electron.

Millikan's value was extremely close to today's International System ( SI ) definition :

By taking the inverse of the above number of coulombs/electron, we get the following result for the number electrons/coulomb :

An alkaline AA battery delivers about 5,000 C of charge during its useful life.

An average bolt of lightning delivers just 15 C but it does so in a mere 30 microseconds!

The Atom

Recall that every charged particle is surrounded by a space ( or field ) that's electromagnetic.  ‘EM’ fields interact, forcing charges away from same polarity charges and toward opposite polarity charges.

Electrons, being lightweight, energetic and negatively charged, are forced toward protons, which are positively charged, heavier and less mobile.

Meanwhile, protons clump together with other protons and also with neutrons—particles made up of 3 quarks having a sum total of zero charge.

These clumps are held together by the strong nuclear force, which is much stronger than the EM force.

An atom consists of one positive clump called a nucleus surrounded by a cloud of attracted, negatively charged electrons.

The diameter of a nucleus ranges from about 1.6 – 15 femtometers ( fm ) a.k.a. ‘Fermi’ in honor of nuclear physicist Enrico Fermi.

Why Don't the Negative Electrons
Stick to the Positive Nucleus?

Well, in 1924, Louis de Broglie, a French physics graduate student, delivered a thesis to Paris University containing his important findings attributing wavelengths to electrons.

It was already known that light waves could behave as particles, called photons, and de Broglie reasoned that nature was symmetric.  Why shouldn't particles behave as waves?

In 1929, after the wave nature of electrons was demonstrated experimentally, the Nobel Prize for Physics was conferred on de Broglie for his discovery.

The “de Broglie” wavelength of a particle is inversely proportional to its momentum :

Using equation [1], we can calculate that an electron traveling at a reasonable speed has a wavelength of about 0.01 nm, (a nanometer is one billionth of a meter).

This length is many thousands of times longer than the nuclear diameter of 1.6 to 15 f m (a femtometer is one quadrillionth of a meter).

So, the electron is much more extended in space than a nucleus.  It can't even exist closer to a nucleus than a couple of electron wavelengths, much less stick to one.

De Broglie wavelengths are usually expressed in nanometer (nm) or Angstrom (Å) subunits :

The Table of Elements

The lightest atom, hydrogen, contains one proton and one electron but weightier atoms can contain over a hundred of each.  Each atomic weight is one element in the periodic table of chemical elements.

Atoms, themselves, can bond electrochemically with other atoms, sharing electrons to form larger molecules, compounds and other materials.

In the end, tennis balls bounce, buildings stand up, and aspirin thins the blood, all because of interacting electromagnetic fields.

It turns out that the metal atoms in the periodic table can bond with each other to form a structure in which many of the atoms' outer electrons are delocalized—that is, they're not tied to any particular atomic nucleus or chemical bond.

Metallic structures resemble a 3-D lattice of positive ions ( atoms lacking an electron ) sitting in a ‘ sea ’ of free electrons that can flow en masse through the structure like water through a sieve.

Metals that support such electron flow are called conductors.  They include silver, gold, copper, tin, nickel, zinc and aluminum.  Metallic alloys like brass, bronze and aluminum bronze, are also conductors.

Materials that don't support electron flow are called insulators.  They include wood, rubber, ceramics, plastic, and glass.

The rate of electron flow is called electric current, symbol ‘ I ’ from the French phrase “ intensité de courant ”.  Current is the amount of charge (q) passing a certain point per second (t):

DC / AC

Direct current (DC) is a one-way flow of electrons.  The intensity of DC may fluctuate but its direction doesn't.

Alternating current (AC) is an electron flow that alternates in direction—the electrons surge forward and back around a center position.

These vibrating electrons create an electric wave of charged particles that propagates through electrical conductors and components.

In the same way, a vibrating speaker cone creates an acoustic wave of air particles that propagates through the air.  Click the link to watch an animation of such longitudinal waves.

Because AC constantly increases, decreases and changes direction, an average, root-mean-square (RMS) value is used to communicate an effective, steady value.

Alternating currents, voltages and power are commonly expressed using RMS values.

Units of Current and Charge

The unit of electric current is the ampere ( or ‘ amp ’ ), abbreviated capital A in honor of French mathematician and physicist André-Marie Ampère (1775-1836), who is considered to be the father of electrodynamics.

In the International System of Units ( SI ), the ampere is the base unit of electricity.

In the SI, one ampere of current is defined to be a flow of 6.241 509 074 × 10¹⁸ elementary charges ( e ) per second.  As stated earlier, that's the number of elementary charges in one coulomb.

In the SI, electric charge ( Q ) is a unit that derives from two base units, current ( I ) and time ( t ):

Equation [3] is a rearrangement of equation [2].

So, the SI defines one coulomb to be the amount of charge that a one ampere current delivers in one second.  So,

For this reason, a coulomb of electric charge is sometimes called an ampere-second.

First of all, voltage is an energy ( symbol E).

What's more, voltage is a potential or stored energy that results from an object's position or arrangement.  Stored energy is not in use but is ready for use.

For example, potential energy rises when particles of opposite charge are separated; also when a rock is raised above Earth.  The rise in energy results from the energy spent in separating the charges or lifting the rock.

A voltage, symbol V, is the difference in electrical potential between two points in an electric field and is defined as energy per unit of charge (q ):

The SI unit of voltage is the volt, abbreviated capital ‘ V ’ in honor of Alessandro Volta—an Italian physicist and chemist who invented the primary battery in 1799.

One volt is one joule of potential difference per coulomb of charge.

A transfer of energy ( or " work " ) can be accomplished quickly or slowly, although doing it quickly takes more power.

For example, it takes more power to run up a hill than to walk up, even though both ways will give you the same amount of stored, gravitational potential.

Power (symbol P) measures an energy transfer per unit of time.  In other words, it's the ‘ speed ’ of energy transfer :

The unit of power is the watt,  One watt is the amount of power it takes to transfer one joule of energy in one second.

Equation [5] can also be written :

In fact, your electric service is ordinarily billed in units of kilowatt-hours ( P × t ) instead of joules ( E).

One kilowatt-hour ( kWh ) is the amount energy transferred by 1,000 watts of power in 1 hour (3,600 seconds).  This amount equals 3.6 megajoules :

An alkaline AA battery delivers about 9 kJ ( 9,000 joules ) of energy in its useful life.

An average bolt of lighting delivers 1,000,000 kJ ( 1 billion joules ) of energy in just 30 microseconds!

Power = Volts × Amps

Take a look at the following algebraic identity, where the two q' s cancel each other out :

Also notice that the above three ratios are the definitions of P, V, and I ( see equations [5], [4], and [2] ).

So, this identity shows that the power P of a current I fueled by a voltage V is :

One watt is the amount of power that drives one amp of current across a potential difference of one volt.

In the ordinary world, there are no perfect conductors of electricity.  Even in metals, electrons collide with ions, losing energy in the form of heat.  This friction-like impedance to electric current is called resistance.

In electronics, resistance can be used to limit an electric current, or to establish a specific voltage.  A resistor is a circuit component that's engineered to provide a precise amount of resistance.

Ohm's Law

Experiments show that the ratio of the voltage V applied across a certain resistor to the current I that gets pushed through that resistor is a constant.

This ratio is defined to be the "resistance" (symbol R) of that resistor :

The unit of resistance is the ohm, abbreviated Ω (capital Omega because Ohm was a person).  A 1 Ω resistor connected across a potential difference of 1 V will let a current of 1 A pass through it.

Equation [8] is called Ohm's Law.  When you multiply both sides of Ohm's Law by I, you find that the voltage across a resistor is equal to the current through the resistor multiplied by its resistance :

And when you divide both sides of equation [9] by R, you find that the current through a resistor is equal to the voltage across the resistor divided by its resistance :

A trick to help remember the three permutations of Ohm's Law (equations [8], [9] and [10]) is to substitute Vulture, Rabbit, and Indian for V, R, and I.

The Rabbit sees the Vulture over the Indian, the Vulture sees the Indian next to the Rabbit, and the Indian sees the Vulture over the Rabbit.

Power Transfer

When electrons flow through a resistor, the resistor must be able to dissipate (move away) all the heat generated by its internal electron-ion collisions.  Otherwise, the resistor will overheat and burn out.

Therefore, every resistor has a power rating specifying the maximum power that the resistor can safely dissipate.

Ohm's Law reveals how much power a certain resistance R must dissipate when a current I flows through it .

In equation [7]  ( P = V × I ) , just replace V with IR :

The Law also reveals how much power a certain resistance R must dissipate when a voltage V is applied across it.

In equation [7], just replace I with V/R :

Resistor Construction

Like garden hoses, wires that are long and thin offer more resistance to current than do ones that are short and fat.

One way to manufacture a resistor is to simply coil up a long, thin piece of wire.

Such wirewound (a.k.a. sandblock or cement) resistors can be very precise and handle large currents.

Other resistors are made from materials like carbon that fall in between a conductor and an insulator.  These materials have relatively few delocalized electrons.

These vintage, carbon composition resistors are composed of tiny carbon particles bound with clay.

Many modern resistors are made from laser-cut, helical tracks of carbon or metal film.