Charge is a fundamental property of some elementary (subatomic) particles of matter.  Charge determines the strength of the particle's coupling to electromagnetic fields.

In a way, this is similar to the mass property that couples particles to gravitational fields.

There are two "polarities" of electric charge, ‘positive’ and ‘negative’, and every charged particle is, itself, the source of an electromagnetic (EM) field.

Physical forces of attraction and repulsion arise from coupled EM fields.

Charged Particles

A variety of elementary particles possess electric charge, including electrons and quarks.

The electron has one elementary, negative charge ( symbol  −e) , whose value is a fundamental physical constant.

The proton is a composite particle comprising 3 fractionally-charged elementary particles called quarks.  Two of the proton's quarks have a charge of +2⁄3 e and one has a charge of −1⁄3 e.  Combined, the three quarks give the proton one elementary, positive 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.

Elementary Charge

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 of Units (SI) definition of the elementary charge e:

By taking the inverse of this number, we get the number of elementary charges in a 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

Surrounding every electric charge is a space (a field) acting to move the charge away from like-polarity charges and toward opposite-polarity charges.

Negatively-charged electrons, being lightweight and energetic, are electrically drawn toward the more massive and more stationary, positively-charged protons.

Meanwhile, protons clump together with other protons and with neutrons (particles comprising three quarks totaling zero charge).  The clumps of matter are held together by the strong nuclear force, which is much stronger than the electric force.

The positively-charged clump of particles (called a nucleus) along with all the attracted, negatively-charged electrons is called an atom.  The gathered electrons repel one another, forming a negative cloud around the nucleus.

The diameter of a nucleus is between 1.6 and 15 femtometers, abbreviated f m.  One fm is also called a fermi in honor of nuclear physicist Enrico Fermi.

Why Don't Electrons
Stick To The Nucleus?

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.

A particle's de Broglie wavelength (symbol lambda λ) is inversely proportional to its momentum :

●  NOTE :  Equation [1] also converts light wavelength to its photon momentum.  Although photons have no mass, they have momentum thanks to quantum mechanics.

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

●  An electron traveling at a reasonable speed has a wavelength of about 0.01 nm, thousands of times longer than the 1.6 to 15 f m diameter of an atomic nucleus.

●  So, because the electron is comparatively spread out over space, it can't even exist closer than a couple wavelengths to a nucleus, much less stick to one.

The Elements

Hydrogen, the lightest atom, has one proton and one electron.  Heavier atoms have over a hundred of each.  Each atomic size is one element in the periodic table of chemical elements.

Atoms can electrically bond with other atoms, sharing their electrons to form larger molecules, compounds, and other fancy stuff.

Tennis balls bounce, buildings stand, and aspirin thins the blood, all thanks to electric charge.

In the periodic table, the metal elements bond into structures wherein many of the atoms' outer electrons are delocalized.  That is. they aren't tied to any particular atomic nucleus or chemical bond.

The metallic structure resembles a fixed lattice of positive ions (atoms lacking an electron) sitting in a ‘sea’ of mobile electrons that can move en masse through the lattice like water through a sieve.

Materials that support the flow of electronic charges are called conductors and they include copper, tin, nickel, silver, and gold.

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

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

AC / DC

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

Alternating current (AC) is electron motion that alternates in its direction.  In AC, electrons vibrate forward and back around a center position.

This vibration propagates a longitudinal electric wave of charge compression and rarefaction that can travel through electrical conductors and components.

This is similar to how a vibrating speaker cone creates a longitudinal acoustic wave of vibrating air particles and pressure.

Since an alternating current is always increasing, decreasing and changing direction, an averaging method called root-mean-square (RMS) is used to ascribe a fixed value to the current's energy.

AC current, voltage and power are ordinarily expressed using RMS values.

Units of Current and Charge

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

The ampere is the base unit of electricity in the International System of Units (SI).

The SI defines an ampere to be a flow of 6.241 509 074 × 10¹⁸elementary charges per second.  As stated earlier, that's the number of elementary charges in one coulomb.

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

So, one coulomb ( 1 C ) is defined as the amount of electric charge delivered by one ampere in one second :

●  A coulomb is sometimes called an ampere-second.

Voltage is an energy.  The unit of energy (symbol ‘E’) is the joule , abbreviated capital ‘ J ’ in honor of James Prescott Joule, a 19th century English physicist, mathematician and brewer who related heat to mechanical energy, laying the foundation for the law of energy conservation.

Potential energy arises from separated charge just as it does from a rock separated from the ground.  The rise in energy comes from the energy spent in separating the charge or lifting the rock.

Voltage (V) is a measure of the electric energy per coulomb of charge (q) :

The 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 energy per coulomb of charge.

Voltage is sometimes called an electro-motive force (emf ) because it can change an object's motion by transferring energy to it.

Despite its name, however, emf is not a force but rather a potential source of energy, like a stretched rubber band.

The transfer of energy (i.e., work) can be accomplished quickly or slowly, though 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 gain you the same amount of gravitational energy.

Power (symbol P) measures energy transfer per time.  In other words, It's the speed of energy transfer :

The unit of power is the watt, abbreviated W, for James Watt (1736-1819), a Scottish inventor, mechanical engineer and chemist whose improvements to steam engine technology drove the Industrial Revolution.

One watt is the power needed to transfer one joule of energy in one second.  Equation [5] also says that :

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

One kilowatt-hour ( kWh ) of energy is 1,000 watts of power over a 1 hour (3,600 second) time span, which comes to 3.6 megajoules :

An alkaline AA battery delivers about 9,000 joules ( 9 kJ ) of energy in its useful life.  An average bolt of lighting delivers 1,000,000 kJ in just 30 microseconds!

Power = Volts × Amps

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

Since the above three ratios are the definitions of P, V, and I ( see equations [5], [4], and [2] ), we see that the power P of an electric current I driven by a potential energy V is :

So, one amp of current across one volt of voltage generates one watt of power.

In the ordinary world, there are no perfect conductors of electric current.  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 currents and to establish potential differences.  Components called resistors are engineered to provide precise amounts of resistance.

Ohm's Law

Experiments show that the ratio of the voltage V across a certain resistor to the current I flowing through it is a constant.

This constant ratio is defined to be the resistor's resistance (symbol R) :

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

Equation [8] is called Ohm's Law.  Multiply both sides of Ohm's Law by I to find that the voltage across a resistor equals the current through the resistor multiplied by the resistance :

Divide both sides of equation [9] by R to find that the current through a resistor equals the applied voltage divided by the resistance :

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

The Vulture sees the Indian beside the Rabbit.  The Rabbit sees the Vulture over the Indian, and the Indian sees the Vulture over the Rabbit.

Power Dissipation

A resistor must be able to dissipate all the heat generated by the internal electron-ion collisions; otherwise, it'll overheat and burn out.  Therefore, each resistor has a power rating.

In equation [7]  ( P = V × I ) , we can use Ohm's Law to replace V with IR and thus find out how much power a certain resistance R  must shed when a current I flows through it :

Or we can use Ohm's Law to replace I with V/R to find out how much power the resistance R must shed when a voltage V is applied across it :

Resistor Construction

Like garden hoses, conductive 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 precise and can handle large currents.

Other resistors are constructed from a material, such as carbon, which falls between a conductor and an insulator.  As such, carbon has 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.