The beginning of electricity:

In the year 1800 the first battery ever is presented to Napoleon Bonaparte and the world changes.

At that time it was the believe that frog legs and metal rods creates electricity. To prove a point that this was not true Mr. Volta built the first electrical "generator" which we can say is a battery.

And this is how it came to be that he held a demonstration for Mr. Napoleon Bonaparte...starting a new evolution in technology that will soon touch each and every person on this planet. Amazing.

And for his great incidental work the unit for a potential difference (electricity) is named after him....VOLTS. 

He also defined capacitance with "Volta's Law of Capacitance".

His Work:

If we achieve a potential difference between two points then electricity is created electricity.

The nicest explanation I have found to explain potential difference is from my "Electrical Trade Theory" handbook by C. du Preez.

If one end of a copper wire is heated and the other remains cold then there is a "potential" for the heated point to transfer to the cold area.

Likewise for electricity:- If between any two points there is a higher charge than the other, then a potential difference exist between them. We measure this in volts.

Volta's law of capacitance law:

Capacitance = Q(charge stored)/V(voltage applied)

This is much better explained if we change the equation to: Q = V * C

The voltage and the capacitance is directly proportional to the final charge(Q).

tba Gary

The first clue is that we say electricity "flows" - yet it is not flowing anywhere. We might be passing electrons but that is as far as it goes.

So, in this time in history and prior - it was still taken for granted that electricity is a fluid...really!

And since a fluid flows, so electricity must also flow...and thus it flows like a river in the wire...and anything that flows has a current.

What a cool reveal that was!

I suspect in Mr. Ben Franklin's time already it was deduced, from his kite experiment (which proved lightning is also electricity), that one part (the clouds) gets charged with something and the other not (the earth), and so it , quite correctly, acquires a potential difference said to have a "charge".

Mathematician, school teacher.

Next to Mr. Volta, Mr. Ohm is probably the best known surnames in the electrical world - unit of resistance and two laws directly carries his name.

All electricity 101 classes start with his lectures.

The electrochemical cell, invented by Italian scientist Alessandro Volta is what got Mr. Ohm started.

Using this volt-cell as a supply with his own invented equipment Mr. Ohm came to realise the relationships between volts, amps and resistance.

Remember: - Electricity as we know it today does not exist yet...they are only playing with batteries here.

His work:

V=I*R i.e. I=V/R i.e. R=V/I

What Mr. Ohm realised is that there is something in the wiring circuit and that something causes ONLY a specific current to flow according to its value. It phantomly controls the current - it is "resisting" the full current to flow...and without further redo named it "resistance".

He discovered was for a specific applied voltage the current changes as a function of the circuit resistance. Hence: V = IR

But Gary...where does that R fit in?

We can also say: If, for an applied voltage of 1Volt, results in a current flow of 1Amp then the resistance of the circuit will be found to be 1 Ohm. Thus R=V/I.

Yes that makes much more sense.

In this equation lies the proof that the circuit must have a certain characteristic and Mr. Ohm called it "resistance".

This earned him the unit of resistance named after him.

Lucky for us its a short German surname.

Info note:

It has come to be that the electronics industry is built on the principles of understanding the beauty of resistance and therefore has a full range of resistors in varying wattages, for without this electronics, as we know it, could not exist.

Oh, by the way...nowadays we can measure resistance with a meter.

We have also developed a code to indicate the resistance value.

When I was just a appy I came up with this rhyme to remember the values of the colours:

Black Broy gave Bev a grey whip

- See if you can figure how the code work from this clue:  1000 Ohms   Colours: Brown Black Red

Now one would have thought that's the end of it...but there is a much more complicated "new" system out there which I'm not going

to cover...it's for special low tolerances and military spec resistors. I seldom encounter and never had to use them...thankfully.

Now back to work:

In Denmark - a country in the strange tip of northern Europe - Mr Oersted powered a wire circuit with Mr. Volta's cell and noticed, whether by accident or not, that it caused a compass needle to deflect and point perpendicular to the wire.

And if the supply around (positive and negative), it deflected the opposite way.

He must have thought there was ghosts in the room...through the air it can talk to the compass needle.

He discovered the connection between electric current and magnetism, and  "electromagnetism" was born.

His Work:

Rule 1: For a straight conductor pointing away from us - if we allow a conductor current to also flow away from us (north closest to us - conventional current) a circular magnetic field around the wire and in a clockwise direction.

To make it easy to remember we use the left hand rule. In a fist grasping a current carrying conductor, if the thumb point towards the positive of the supply (the direction electrons are flowing) the rest of the fingers will in the field direction.

Rule 2: If a current carrying conductor is coiled (looped) it creates a magnetic field around the coil with lines entering the bottom opening (south pole) - which is also the entry side for the conductor current flow - and exiting top opening (north pole). 

Rule 3: The field strength is proportional to the amount of current.

Rule 4: In a coiled wire (solenoid) the more coils(loops) the stronger the field.

I am so grateful for project Gutenburg to have had this in their library.

If one wants to undermine your own intelligence then read this piece and feel what I felt. 

If a current carrying conductor is brought into a magnetic field a force exerted this conductor, causing it to move.

If the currents flow in the same direction the field will be stronger (added) and attract each other.

If the current flows are opposite then the field will work against each other (subtract) and repel each other. 

The left hand rule also applies here - (but you said the right hand rule in the heading)

To the clever ones who practice integration:

I have come across many educational institutions that claim that in two parallel wires with opposite flowing currents having intersecting electromagnetic fields, the fields cancel out one another?

Really, why is that not what I see in my head?

In my head I see the two fields - having abundance of the same charge (positive or negative) therefore they cannot equalise in anyway, meaning they cannot occupy the same space, this will have the repelling affect as we are familiar in magnetism. The fields will compact between the wires and balloon out on the extremities.

If they were cancelling out I don't think we would experience any repelling force between the wires.

But then I thought...Of course if one was to put a ferro - metal close to the north or south pole of the contraption it would seem there is no magnetic force - but that's not because its not there?

Ahhh, maybe from that perspective we say it cancels out, the magnetic force is decreased to nothing.

Though my point still stands...but I guess we will never know since these lines don't really exist...only the effects of it is observable.

So to the clever guys...or does the fields diminish. (cancel out?)

This answer was provided by Mr. Michael Faraday 

Mr. Michael Faraday brought it all into practical use and open the doors to our new civilisation the way it is today. He opened the door.

And all that from someone with no formal education...apparently only "basic algebra" knowledge.

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His birth-year 1791 - In 1991 it has been 200 years ONLY!

Mr. Faraday discovered "electrical induction " and completed the work with just about all prominent uses, as is it is today.

From the transformer to the electrical motor, so one can safely say he was the first electrician.

Whenever we hear induction, we should reflect back and say: Thank you Mr. Faraday.

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This was the big breakthrough - the stage for the real beginning of the electrical evolution was set.
 

The clever professors of those days had pretty elaborate experiment equipment but here is an electricians (DIY / backyard) version proving the concepts of electro-magnetism.

There we go...it moves pretty strongly with the starter motor current.

The "flexible wire" is 2.5 mm2 cab tyre with enough slack to move in all directions. 

But what do we get from this experiment mostly?

If you noticed the change in direction of the hands and the after effects then the mission is accomplished!

The direction of forces changes if any field direction changes (the magnet or the current).

This is also a beautiful example of how the hand can be used to remember the direction of the fields.

*In those days it was the right hand rule, so to avoid confusing I stick with the left hand only. If you are in the acedemia just remember the right hand is opposite and the thumb points to the wrong negative pole..

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Work:

Understanding the nature of the dynamics of magnetic and electric -fields (Elementary/ Basic):

But what if we looped this same wire?

and what if we looped it many times?

That's when the realisation came that electro-magnetism took on the same characteristics of a magnetic field.

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When I saw this result from professor  it made perfect sense and it became the basis of my understanding of it.

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How strong is strong?

Wilhelm Eduard Weber: German Doctor. 1804 – 1891

First use of c for speed of light
Work on magnetism
Electrodynamometer
Telegraphy

His work:

Mr Weber (I call him doctor induction) created a platform for us to quantify magnetic fields.

He made it possible for scientists and electricians alike to understand the relationship between electricity and magnetism.

Like his hand rule:

***This is a slight modification from the left-hand rule we already know. As soon as you get it - you will never forget it.  

Easy one: Grab a coil with the left hand, with the fingers pointing in the direction of the coil's current flow then the the thumb will be pointing to the north pole (the direction of the flux flow)

Complicated one: Grab a coil with the right hand and the fingers pointing to CONVENTIONAL CURRENT FLOW then the thumb will be pointing to the north pole of the electric field. 

In order to visualise the invisible force we needed a unit to quantify the electrical force field...He called it flux.

Why?  

The word flux literally means: "to flow / emanate from" and / or "an unsure state of change". This is exactly how the electro-motive-force can be described.

And in his honour...flux is measured in Weber(Wb).

Definition: A weber ( Φ or Φ_{B )} is the magnetic flux when linking a circuit of 1 turn produces an emf of 1Volt in it, when it is is uniformly reduced to zero over 1sec.

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To get there we have to start right at the beginning:

 The chemistry of all things...

But before we start - just by the way - since it is so intriguing: -

According to contemporaries - Matter is anything and everything that is(exist).

The smallest identifiable part of matter is a molecule. So one can say matter is made up of molecules.

The smallest identifiable part of a molecule is an atom. So one can say molecules are made up of different atoms.

In the atom the electrons - like the planets of a galaxy - orbit a nucleus (the sun).

How big are atoms - (0.1 to 0.5nm), i.e.  a million times smaller then diameter of a human hair (0.1mm) strand.

I also saw a reference where it is said that 99.999999999999% of an atom's volume is empty! Nothing. One would wonder what keeps it all together.

The electron inner orbits are spherical but as the distance grow the pathways becomes less predictable.

The electron cloud has a radius 10,000 times greater than the nucleus.

The nucleus is made up of protons (and now neutrons).

From more than one resource it was said that a proton mass is approximately 1800 times that of a neutron. The neutrons mass is slightly higher than a proton.

Apparently and more spectacularly the electron, for hydrogen, are spinning around the nucleus at 2.2 km/sec.

The arrangement and quantities of these elements (electrons/protons/neutrons) determine ALL chemical elements. For the chemists this is their bread and butter.

And this is where it gets  interesting for the electrician: The electrons are negatively charged and the protons are positively charged. The neutron don't want to be part of the game, they are "neutral".

Electrostatics:

At atomic level the movement of the electrons makes up the characteristics of the different material such as when there is equals electrons and protons it carries no charge - the natural state of materials - unless it is a magnet!

The nucleus is held together by the tight pull of what is known to chemists and physicists as the "strong force."

On the other hand the the negative electrons is attracted to the nucleus (opposites attract) and nucleus is known as the electrostatic force.

This effect of opposites attract and similar charges repel each other is referred to as the First Law of Electrostatics.

For some materials - such as copper - An applied emf will dislodge electrons in a specific direction from atom to atom and this is our flow of electricity and from this various other forms of energies can be derived. 

What is an electrical charge?

When I found this information it just blew me away...it is not the norm in the educational system... yet I believe it is the "more truer" version of the definition of units and measurements.

An object’s electrical charge is determined by the number of electrons that the object has gained or lost. Because such a large number of electrons move, a unit called the "coulomb" is used to indicate the charge.

One coulomb is equal to 6.28 x 10e18(billion, billion) electrons.

For example, if an object gains one coulomb of negative charge, it has gained 6,280,000,000,000,000,000 extra electrons.

More conventionally : A volt is defined as a difference of potential causing one coulomb of current to do one joule of work.

A volt is also defined as that amount of force required to force one ampere of current through one ohm of resistance.

In the electrical world:

Now we need to put on the thinking hat, for all the work from all our scientists is coming to fruition in the maths of things. For a scientist if it cannot be proven via the maths then its not a fact yet.

We can see all the effect of magnetic forces but can we prove it by calculation?

I get the impression this is what Mr. Maxwell was good at - he could see the maths in things.

The stronger the magnetic field the more force it seems to be able to exert...so lets start there. We need a way to define that force (Newtons) that we see magnetic filed at work.

We say flux is that that generates 1V, but we don't know how big, it could be as big as a house or as small as a hair and still it provide 1V.

If we want to calculate the effects of flux, we need a better way to define this flux.

It does not really have lines but what if we said: The flux per a particular area - after all it will give us an idea of how concentrated it is...which is a function of the force it presents. Now that is a great idea. 

Flux by itself means nothing much...but if we can define its concentrate per area that is the function of its force...so:

Flux density B = Flux / Area =    Φ / m2 - and in order to pay tribute to the great inventor Mr. Nikola Tesla - the unit of flux density is Tesla (T).

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What will be the force on a conductor if we placed it in the electro-magnetic field of another conductor (the field intersecting perpendicular only)?

Three factors come into play:

1. How strong is the magnetic field it finds itself in - i.e. flux density.
2. How much current is flowing in the conductor - this determines its own field strength
3. and the length of the conductor in the field.

This is also true for the magnetic circuit where the magnetising force (H) at a specific point in the field will be a specific force and it will also be equal to:

H = IN/L amps/mtr

I = The current that creates the force.

N = number of turns

L = length of the magnetic circuit

*some letters should be in small caps but it will create confusion in this doc.

emf = F * d joules.

and if we bring in the time it took

1: The applied voltage and

2: The amount of current in the circuit.

So the formula for work is F =  V * I and is measured in watt.      

Is power work done?

No. Power is that what is required to sustain a (re)action.

Work done is a measure of much energy was consumed/used/exerted over a period of time...we will still get there.

Weber = flux  = V * t

i.e V = weber / t or more specifically V = dΦ /dt

So far we have assumed on conductor but what if e start having more then one conductor:

emf V = Number of conductors * dΦ /dt =  d(N*Φ)/t Volt

Work done = F * d N.m.

i.e. Wd = BIL * d

But energy = WD /sec so if our conductor moved over 1 sec then suddenly we know how much energy was exerted.

i.e. Power = BIL * d/sec

Oh, but hang on ...d/sec =  mtr/sec = velocity!

So Power = BILv Watt

BILv = VI

Cancel the currents and we have: V = BLv volts.

*It is imperative to remember that this is for ONE CONDUCTOR  cutting the magnetic lines - we worked on the premise of the definition of a Weber.

For a coil Total emf = BLv * number of turns volts(N).

It is also imperative to remember this formula only accounts for perpendicular crossing (maximum) of the magnetic lines.

In reality magnetic lines are crossed according to the sine of the angle meaning the instantaneous values would be emf = BLvN * sin Φ volts - that angle at that particular time.

So now we can generate AC wave forms:

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So far for this formula emf = BLv*(N) we have one conductor and it moves linearly

We have to improve it to cover a rotating conductor and also for a looped conductor . The v in this formula implies linear movement (distance) for a motor we have to relate the formula in rotational velocity.

The L also represent a straight one conductor 

See here to perfectly understand the concepts of calculations in circles as used in the AC waveform.

See here for the graphical representation of the AC wave form.

We are now interested to find out how fast our waveform is being formed, and this is where radians comes to our rescue with angular velocity.

Linear velocity (v) = m/s but in terms of radians the distance per revolution (angular velocity) would be 2*Pi thus 2 * Pi /time for one revolution.

For multiple revolutions = 2Pi * number of revolutions/sec (n).

v = 2 * Pi * n   rev/sec

emf = BL(2*Pi*n/sec) N * sin Φ volts = 2Pi*BLnN/time sinΦ volt

Now we have to improve L.

A loop can be calculated as total length + width(w) and this is the same as the area formula(A) the loop forms.

e = 2Pi*B(L*w)* n * N sinΦ volt

The total emf generated at a specific instance (instantaneous value) during the rotation of a COILL:  e = 2Pi*BA* n * N sinΦ volt and the result always completes an alternating sine wave form.

A cycle is one complete positive +negative part of the waveform.

And this is where the mains frequency of 50 hz (Europe) and 60 Hertz (America) comes from.

Average value of a PURE AC wave form = 0.636 Max value

and 0.707Max value is the RMS value...

Ask an electrician where this comes from and a shrug might be the best answer.

So Average value:

It is at it is in maths: Add the number of points you want to average and divide it by the qty of these points. Lets say current:

Iave = (i1+ i2+i3+in)/n (the number of instantaneous values one cares to calculate)

By the way : If we took the average over a PURE full cycle what will the answer be : 0...they will equal out. So we only calculate over half a cycle.

For my tests I made Imax = 100 - so one gets an impression of percentage.

At only 90Degree peak value it is 100/2 = 50. That's way off from 0.636?

Then I tried it at 30degree intervals - answer 62.20084679...closer but not there yet.

Then I tried it at 10 degree intervals. Answer = 63.50029057

And at 5degree intervals: Answer = 63.62157097

Why did I do this?

I found  2/Pi arrive at 0.636....why?

This was arrived at by using calculus.

Calculus is a method (tool) to calculate to the smallest possible increment...which is exactly what we are looking for in our averaging venture.

In this case the total half cycle (remember why only half cycle: they cancel out over a full cycle) are is calculated and then divided by the smallest incriment (that is the length of the half cycle).

The area of say the positive cycle is:

A = ⌠Pi i . dΦ

      ⌡0

a = ⌠Pi i . dΦ .....

      ⌡0

= Max * ⌠Pi  sinΦ .dΦ

             ⌡0

= -Max * [cosΦ] between Pi and 0

= - Max * [-1-1]

=2Max in Ampere-radians

*See calculus for base information (hopefully I can find  a maths fundi volunteer one day)

If we know the area is 2Max
and we know the length is Pi...see here why?      
    

We have a calculation: Average = 2Max/Pi.

which result in:

Iaverage = 0.636 * Imax or

Vaverage = 0.636 * Vmax

Do not forget these are for pure (proper) sine waves only.

The standard AC voltages 220V or 110V or 400V - where does it all come from?

Even better - When we meter an AC circuit we measure these standard values...But if the supply is a waveform meaning it is not stable (static) then what exactly are we measuring.

When we purchase electricity it is not measured on the basis of average or peak but on the basis of the work it does for us. 

When we size and electrical appliance it is on the basis of the kiloWatt it can deliver for us. It is for this reason we need a method to measure the work an AC supply can deliver for us.

There we go again with our average for the AC waveform, but this time on the premise of power.

Thus: P = VI = I²R(i1² * R  +  i1² * R +  i2² * R +  i3² * R +  in² * R)/n

But R is the same at all times so:

I² = (i1²  +  i1² +  i2² +  i3² +  in²)/n

I don't know if the mathematics quadratic formula exist from this or from some other spectrum but it is called the quadratic formula...and on this basis electricians call it the ROOT MEANS SQUARE.

Now I am an electrician and uses this everyday of my life, like forever, so when I hear this value it causes a tingling in my spirit. Exciting stuff.

The RMS value is the value we all use and gets invoiced against.

I did the actual calculations...

But just in case we hear the words: "What will I ever need calculus for in life?" - Here is another example of its eloquence.

From our previous average calculation we know 

Average = Pi/2 * Max

i.e for Iave = Pi/2 * Imax

In terms of power it will be P = I^{2 *} R = 2/Pi * (i^max2) R - the power area of the curve.

to calculate the average for power on a half cycle:   [2/Pi * (i^max2) R]/Pi

since R same on left and right they cancel...and the Pui cancels

and we simplify the quadrature

I² = 2/Pi * (i^max2)

Iave  = Imax/√2

= 0.707 Imax

To calculate the peak value from RMS: Peak = 1/0.707 * RMS

Form factor =0.707/0.636 =1.11

Charles-Augustin de Coulomb - French(1736 - 1806)

Completed the description of the electrostatic force.

Coulomb's law states that: 'The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to:

1: The product of the magnitudes of charges

2: and inversely proportional to the square of the distance between them.

If charges of the same polarity repel each other; charges of opposite polarity attract each other.

F = k * (q1*q2/d²)  *d can be r - it is just the distance between the conductors.

k = Coulomb constant 9×10⁹ N.m^2.C⁻²

q1 and q2 the charges

r = d = distance between the charges

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