Electric charge is a fundamental property of some particles of matter, for example, electrons and quarks.  Charge can have a polarity of either negative or positive.

An electron is an elementary particle having one negative elementary charge (symbol-e).  A proton, composed of three electrically charged quarks, has one net positive charge (+e).

The mathematical symbol for charge is q, from the 18th century phrase "quantity of electricity".  The standard unit of electric charge is the coulomb, abbreviated C (capital C because Coulomb was a person).

Around 1910, Robert Millikan became the first person to measure the elementary charge, a fundamental physical constant.  His value was extremely close to today's definition :

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 just 30 microseconds!

The Atom

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

Electrons, being lightweight and energetic, are electrically attracted toward the more massive and stationary protons.

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

The positive clump of particles (called a nucleus) and all its attracted electrons is called an atom.  The attracted 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.  A femtometer is also called a fermi, in honor of nuclear physicist Enrico Fermi.

Why Don't Electrons
Stick To The Nucleus?

In 1923, Louis de Broglie, a French physics graduate student, presented his 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 :

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

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

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.

Because it's so spread out in comparison, an electron can't even exist closer than a couple of electron wavelengths from 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, themselves, can bond together by sharing electrons, forming 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 where many electrons are delocalized.  That is, they aren't dedicated to any particular atom or chemical bond.  Metallic structures have a lattice of positive ions (atoms lacking one electron) sitting in a "sea" of mobile electrons.

The mobile electrons can flow en masse through the lattice much like water flows through a sieve.  The rate of flow of this electric charge is called electric current, symbol I, from the French phrase "intensité de courant".

So, current (I) is the amount of charge (q) passing a certain point per unit of time (t) :

The unit of electric current is the ampere or amp, abbreviated A (capital A because André-Marie Ampère was a person). 

Materials that support electric current, such as copper, tin, nickel, silver, and gold, are called conductors.

Materials that don't support electric current, such as wood, rubber, ceramics, plastic, and glass are called insulators.

Potential energy arises whenever opposite electric charges are separated, just as it does when a stone is lifted off the earth.  The energy rise comes from the energy spent in separating the charge or lifting the stone.

The unit of energy (symbol E) is the joule (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.

Electrical voltage (symbol V) is defined as the potential energy of separated charge, per unit of charge (q) :

The unit of measurement for voltage is the volt (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 electromotive force (emf ) because it can change an object's motion by transferring energy to it.  Despite this name, however, emf is not a force but rather a potential energy.

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

Power (symbol P) is thus defined as energy transfer per time.  In other words, It's the quickness of energy transfer :

The unit of measurement for power is the watt, abbreviated W (capital W because Watt was a person).  1 W is the power needed to transfer 1 joule of energy in 1 second.

Equation [4] can also be written :

In fact, your electric service is ordinarily billed in units of kilowatt-hours (P × t), not joules.

One kilowatt-hour (kWh) is 1,000 watts of power for 1 hour (3,600 seconds), making the total transfer of energy equal to 3.6 megajoules :

An alkaline AA battery delivers 9 kilojoules (k J) of energy in its useful life.  An average bolt of lighting delivers 1,000,000 k J 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 [4], [3], and [2] ), we see that the power P of an electric current I flowing across a voltage V is :

One amp of current across a one volt energy difference equals 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.  So, 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 [7] 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, times the resistance :

Divide both sides of equation [8] 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 permutations of Ohm's Law (equations [7], [8] and [9]) 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 [6]  (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, conductors 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 coil up a long, thin piece of wire.

Wirewound resistors can be precise and also handle large currents.

Other resistors are constructed from a material, such as carbon, that falls in between a conductor and an insulator.  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.