Series parallel anecdote

Series parallel anecdote

Finally we arrived...in the here and now...lets learn the art of electricity from an electricians point of view..

So now we know all about the circuits - what now?

In real life it was found all loads have two wires that we connect the voltage to...but we can also connect them in different configurations to the supply.

If you have a thing-a-magic (load) - with two wires how can you connect them?

We can connect them like a train...one end to the next following each other.

This is the series connection.

The word literally means: "A series of events one after the other"...like a film series. And so it is only logical that we also call this a series connection.

Clever scientists we have.

Parallel connection:- But we can also connect it wire to wire...to form a ladder.

Guess what...the word parallel literally means "events happening at the same time"..."they are running in parallel with each other"...It is only logical that our ladder connection is referred to as parallel connection.

Yep, as I said, Real clever boys...no other word can describe that connection.

Now how does this tie into Mr. Ohms observations.

If I connect resistors in series what happens?

What happens when resistors connected in parallel?

Electricity (same as its primordial cousin magnetism) exist in another dimension to our senses. We cannot see, feel or touch it, but we can perceive the result of its presence.

So, to make it real, especially for some of us - like me - that battle to see the maths in life, by using an analogy to grasp the concept of electricity.

Analogy: Trains and people.

In our trains there are only front and back doors to our compartments, including the first and last compartments.

Our trains does not have an engine, we have to paddle it to make it move.

Every day a certain amount of people will depart and go and do what they have to do - visit their aunts, go to work, go to school - wherever, but at the end of the day all trains and all the people return to the platform they departed from. The point is they are always one part of a big connected system and some laws can be derived from this.

Examples are:

	The rails of trains always connect them together to all platforms. This makes one big system.
	A train can be one compartment or many compartments.
	To move a train requires a certain amount of energy to move. No more and no less.
	The following real life scenarios qualifies in all respect to electrical connections.
	1: Series : The different compartments in series separate the people, meaning they cannot get to the external (front/back) doors.
	1: Parallel: In parallel all people are at the external doors. One can say there is no separation - all hands are on deck / available.

Note: * In real life - Small drive systems are put in series in order to reach a higher output potential. Like batteries - connect two 12V batteries in series and we get 24V on the output terminal

*In real life - to increase the capacity (how much power is available) of a system (engine) we put engines in parallel but they MUST HAVE THE SAME OUTPUT POTENTIAL. Two parallel connected 12V batteries provides us twice the amount of power (current).

Remember - In this story the people are the engine to the train - they paddle it. So in compartments with less people - each person will have to work harder than those with more people in the compartment. If we add the contribution of work from every person we can calculate how much energy it takes to move each train.

Ps: Who sets this amount of energy required for any train to start moving, the people or God?

Finally I am sure this analogy can be broadened to a global system and it will still hold true for all electrical rules as well.

This can grow in its own pace if there are those interested in contemplating this further, to see where does it break.

For physicists I can see how this can be used as visual aid to represent the characteristics of all kinds of electrical phenomena including inductance and capacitance etc.

That's it we are set.

Voltage = Number of people (especially separated or not).

Every train compartment represent a load (resistance) as in the real life.

Resistance = The total size of all the bodies in each compartment. 100 thin people low resistance, 100 fat people high resistance.

Current = The energy required to move the train.

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Understanding the parallel connection:

Looking at the platform all trains parked are parallel connected.

Any amount of people can board any train, so each train will have a percentage portion of the total amount of people. Though each train has its own amount of people they are not compartmentalised (separated) so we can say all the people is available from all trains.

Voltage: All the people is "available" in parallel so voltage stays the same.

On the other hand - The more people per train the less energy each person have to exert (current) to move that train, this means less current, less wattage per compartment.

Conclusion: The voltage in a parallel connection is the same across the circuit rails. The branch current (train) changes according to the value of the total resistance (types of people) of each branch.

Understanding the parallel resistance:

In a parallel connection all connections (resistances) are at rail voltage, this means the voltage is the same for all circuits.

For each circuit we can then say: Ix = V/Rx

We also know that It (the total current to the circuit) = The sum of all the branch circuit currents, ie. It = I1 +I2 +In

Therefore: V/Rt = V/R1 + V/R2 + V/In...

We can simplify this by the V on the left cancel out with V on right.

AND WE ARE LEFT WITH:

Total parallel resistance formula: 1/Rt = 1/R1 + 1/R2 +1/Rn

Now we sit with a mathematical conundrum...

Use the LCD (lowest Common Denominator or Highest Common Denominator) math principles to work out resistance.

Method: R1 X R2 X Rn = Common Denominator. (CD)

then Rt = 1/ [(1 x R2XRn)/CD + (1 x R1XRn)/CD + (1 x R1XR2)/CD)]

As you practice this you will begin to see certain "math" certainties like:

If the resistors all equal the just divide the resistance by the number of resistors.

Another shortcut FOR ONLY TWO RESISTORS if one cares to remember is:

Rt = R1*R2/R1+R2 - I never figured out the mathematical root of this.

Understanding the series connection:

If 100 people get into one train...they are dispersed in different quantities in each compartment.

Voltage: More people - more voltage - less people, less voltage per compartment.

Current: In order to move the train each compartment MUST contribute the same amount of energy - no more, no less. Otherwise the train will break apart.

Power: More people more power, similarly - more energy from the people more power generated.

Conclusion: The voltage (people) drops according to the value of each resistance. The current (energy) in a series connection is the same across the circuit.

But adding the voltages across each section (compartment) will always amount to the applied voltage (100 people).

Amazingly this analogy rings true into the finest detail of circuit analyses.

Series calculations:

Vt = V1+ V2+ Vn

ie I*Rt = I*R1 + I*R2 + I*Rn

and if the I cancels out on left and right then:

Series total resistance: Rt = R1 + R2 + Rn

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Function: y=(x)(x)	1	2	3	4	5	6	7
	1	4	9	16	25	36	49

Diff. function (change only)	1	2	3	4	5	6	7
differential (dy/dx=2x)	2	4	6	8	10	12	14

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