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Electricity What's
Charge Is Fundamental



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 :

e ≡ 1.602 176 634 x 10 -19 C

Inversely, 1 C ≅ 6¼ billion billion electrons


AA Battery


An alkaline AA battery delivers about 5,000 C 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 (an electric field) acting to move the charge toward opposite polarities and away from like polarities.

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.  The particles are held together by the strong nuclear force, which is much stronger than the electric force.

The positive clump of particles (called the nucleus) and all its attracted electrons is called an atom.  The 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.

1 f m (or fermi) = 1 quadrillionth (10 -15 ) of a meter



The Atomic Nucleus, Surrounded by a Cloud of Electrons




Why Don't Electrons
Stick To The Nucleus?


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


λ = h/p [1]


λ = the particle's wavelength, in meters
p = the particle's momentum (mass × velocity), in kg⋅m ⁄ s
ℎ = Planck's constant ≡ 6.626 070 15 × 10 -34 kg⋅m2 ⁄ s


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

1 nm = 10 -9  m            1 Å = 10 -10  m


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 diameter of a nucleus (1.6 - 15 fm).

As a result, electrons can't even exist closer to a nucleus than a couple of electron wavelengths, 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 the chemical elements.

Chemical elements bond electrically, sharing electrons to form molecules, compounds, and other fancy stuff.

Tennis Ball

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





Current — Moving Charge



In the periodic table, the metals have many electrons that are delocalized, that is, not dedicated to any particular atom or chemical bond.  The metallic structure is 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 electrical 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 in a period of time (t) :


I = q/t [2]


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.




Voltage — Separated Charge



Potential energy arises whenever opposite electric charges are separated, just as it does when a stone is lifted off the earth.  The energy increase comes from the energy spent 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 stored by separated charges, per unit of charge (q) :


V = E/q [3]


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 alter an object's motion through energy transfer.  Despite the 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 energy.

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


P = E/t [4]


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 :

E = P × t


In fact, energy usage is usually billed by the kilowatt hour (power × time), not by the number of joules.

One kilowatt hour (kWh) is 1000 watts of power for 1 hour (3600 seconds) so its total energy is 3.6 megajoules :

1 kWh = 1000 W x 3600 s = 3,600,000 J = 3.6 MJ of energy


Alkaline AA


An alkaline AA battery delivers 9 kilojoules (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 :


Algebraic identity [5]


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 :


P = VI [6]


So, one watt of power is conveyed by one ampere of current flowing between a charge separation of one volt.







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

In electrical circuits, resistance is used to limit currents and to create 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) :


R = V/I [7]


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 it times the resistance :


V = IR [8]


Divide both sides of equation [8] by R to find that the current through a resistor equals the applied voltage divided by the resistance :


I = V/R [9]


To help remember equations [7], [8] and [9], use the mnemonic of Vulture, Rabbit, and Indian for V, R, and I.  The Vulture sees the Indian next to the Rabbit.  The Rabbit sees the Vulture over the Indian, and the Indian sees the Vulture over the Rabbit.



Power Dissipation



In equation [6], replace V with IR to find the power faced by a resistance R when a current I flows through it :

P = (I^2) x R


Or replace I with V/R in equation [6] to find the power faced by a resistance R when a voltage V is applied across it :

P = (V^2)/R


A resistor must shed the heat generated by electrical power.  If a resistor's power rating isn't high enough to do so, the resistor will overheat and burn out.




Resistor Construction



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


Wirewound cement resistor

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.


Carbon comp resistor


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.

Metal film resistor



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