H

#### [email protected]

- Jan 1, 1970

- 0

[] indicates subscript.

~A means the vector A.

<four> means 4.

9 Electric current similar to water current

Ed 01.12.31 -----------------------------------------

Abstract

--------

A perfect comparison between a closed circuit of water current and a

closed

circuit of electric current is made and Ohm's law is obtained in this

manner and it is shown that, contrary to the current belief, existence

of

conduction current is not because of the existence of any electric

field

in the conductor, and the linear relation ~J=g~E cannot be valid. The

relaxation time (necessary for the current to reach its final speed)

and

the final speed (drift velocity) of the current are obtained in the

above-mentioned manner, and it is shown that, contrary to what is

believed

at present, both of them are independent of the chosen standard unit

charge (eg electron charge or coulomb) and its mass. It is also shown

that, contrary to the current belief, alternating current is steady.

We also prove the existence of a kind of resistance arising from the

configuration of the circuit. Action mechanism of transistor is

explained

and a hydrodynamical analogue for it is introduced: both confirming the

material presented earlier.

I. Introduction

---------------

What is presently propounded as the existence cause of an elrectric

conduction current in a conductor is the existence of some electric

field

arising from the power supply (sourcs) in the conductor and the

response

of the conductor to this field in the form of producing current density

(eg

in the form of ~J=g~E for an ohmic material). In other words it is

thought

that existence of the conduction current necessitates existence of an

electrostatic field porducing it, and also existence of the potential

difference necessitates existence of an electrostatic field causing it.

And then an entire similarity is considered between the electrostatics

and

the subject of electric current, eg as in the electrostatics, the curl

of

the above mentioned field is considered equal to zero in the conductor

and

then eg it is tried that a conduction problem to be solved in the same

way

as an electrostatic problem (by obtaining appropriate solution to

Laplace's

equation (see Foundations of Electromagnetic Theory by Reitz, Milford

and

Christy, Addison-Wesley, 1979)).

In this article considering the entire similarity existent between the

electric current and mechanical current of water it is shown that,

really,

existence of the conduction current does not necessitate existence of

any

electrostatic field in the conductor (or wire) carrying the current,

and

the potential difference here is other than the potential difference in

the

electrostatics, and in this manner we obtain Ohm's law.

II. Water circuit and Ohm's law

-------------------------------

Consider the water circuit shown in Fig. 1.

__________________________________________________

| ,---------------------------------, |

| | | |

| | |^^^^` `^^^^^|

| | ||~| |~| |

| | || | | | |

| | || | | | |

| | || | | | |

| | || | | | |

| | || | | | |

| | || | | | |

| | || | | | |

| | _ ||_| |_| |

| | /\`|`/\ |____ _____|

| `-----------|--`+`--|-------------' |

| <------ /`|`\ |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'

Fig. 1. Schematic figure of a water circuit.

This circuit is a closed tube full of water set on a horizontal level

which

its water is being forced to circulate by a pump in the tube.

Suppose that the pump is switched off and the water is motionless. We

want

to see what happens when the pump is switched on. By switching the pump

on,

its blades exert force on the water particles adjacent to them, and

these

particles transfer this force to other particles, and altogether the

water

gains speed gradually. In other words the energy transferred from the

pump

to the water immediately after switching the pump on causes increase in

the

kinetic energy of the water, ie the energy of the pump is conserved as

increase in the kinetic energy of the water. But does the water in each

cycle conserve the energy received from the pump as the increase in the

kinetic energy of itself? If so, we must expect an infinite speed for

the

water after elapsing of enough time, while we know that this is not the

case

and after some time the speed of water reaches a constant limit while

the

pump is still in operation and is giving the water more and more

energy.

So, where does the energy of the pump, which no longer is conserved as

increase in the kinetic energy of the water, go? The answer is that

this

energy is dissipated as heat in different parts of the circuit and the

conservation law of energy remains consistent.

Let's see how every part of the circuit changes the energy of the pump

into

heat when the circulation speed of the water in the circuit has reached

the

constant limit. Imagine a definite drop of the water just when a blade

of

the pump is directly exerting force on it. This drop is propelled by

this

force (but since we have considered the situation of the constant speed

of

the water, this drop does not accelerate due to this force). When the

drop

has been pushed forward a little, the blades of the pump directly exert

force on another equivalent drop which transfers this force directly to

the

previous pushed forward drop. In this same manner it is seen that the

pump

directly and indirectly exerts force on the first drop during its

circulation in the circuit. Since, exerting this force on the drop, the

drop is displaced, this force (being exerted by the pump) performs work

on

the drop. Therefore, the energy of the pump given to the drop is this

same

work performed on the drop which we show it by V and attribute it to

some

potential difference between two relevant points of the circuit (we

mean by

the "potential difference" the work performed on this (standard)

definite

drop by the above mentioned exerted force during the displacement

between

the two points). But we know that this work does not increase the

kinetic

energy of the drop. Thus, what occurs to this work which according to

the

conservation law of energy does not disappear? The answer is that this

work

appears in the form of heat arising from the friction, ie heat arising

from the opposition of the drop to the drops in front of it which

exerting

opposite force (and consequently performing negative work) try to

prevent

the drop from accelerating.

Now let's see how much energy of the pump in every part of the circuit

changes into the heat when the circulation speed of the water in the

circuit has reached the constant limit. Suppose that a part of the

circuit

is as shown in Fig. 2 in which the arrow shows the direction of the

water

flow (or current).

/^^^^^^^^^^^^^^^^^^^^^^^^^/^^^\

,`.` ` ` ` ` ` ` ` ` ` ` `,``/^^^^^^^^^^^^^^^^^^^^^^^^^^/^\

A[1]( . ( ( ---------> ( )A[2]

`, ' . . . . . . . . . . .`,.\__________________________\_/

\,________________________\,_,/ l[2]

l[1]

Fig. 2. Water current in the two tubes is the same, but the force

exerted on a drop in the part l[2] is A[1]/A[2]fold.

Suppose that the two lengths l[1] and l[2] are equal. We want to see

what the

magnitude of the above mentioned force (arising from the pump) exerted

on the

above mentioned standard drop will be in the part l[2] if this force is

F in

the part l[1]. If only the tube shown by the dotted line, which its

cross section is equal to A[2] and is positioning just opposite to the

tube

l[2], was to be displased exerting force on the water of the tube l[2],

the

above mentioned force in the part l[2] would be still the same F. But

the

dotted tube is not the sole one displacing, and it is obvious that all

the

water of the tube l[1] will be displaced entering the tube l[2],

because

the two tubes l[1] and l[2] are in series and the water current, which

we

show it as I, is the same in each. The whole tube l[1] contains, in

number,

A[1]/A[2] tubes each equivalent to the tube l[2], and the situation is

similar to when this number of tubes are set in series and transferring

their

forces to each other finally exert their forces on the tube l[2] (see

Fig. 3).

/^^^^^^^^^^^/^\/^^^^^^^^^^^/^\/^^^^^^^^^^^/^\ /^^^^^^^^^^^/^\

( ( ( ( ( ( )....( ( )

\___________\_/\___________\_/\___________\_/ \___________\_/

l[2]

Fig. 3. Forces of A[1]/A[2] tubes are added together,

exerted on the tube l[2].

It is obvious that in this state the above mentioned force exerted on

the

mentioned drop in the part l[2] is equal to (A[1]/A[2])F. Since the

ratio of

this force to the force exerted on the drop in the part l[1] (ie F) is

equal

to A[1]/A[2], we conclude that the force exerted on the standard drop

is

inversely proportional to the cross-section of the part of the tube in

which

the drop is located. Therefore also the work performed by the mentioned

force exerted on the drop is inversely proportional to the

cross-section of

the part of the tube in which the drop is located, and since we know

that

this work is proportional to the length of the part of the tube having

a

constant cross-section which the drop must travel, altogether this

work is proportional to l/A in which l is the length of the part of the

circuit that has the constant cross-section A. In other words this part

of

the circuit dissipates as heat some energy of the pump which is

proportional

to l/A.

It was cleared that in series parts of the circuit everywhere the ratio

l/A

was more, some more energy of the pump would be dissipated as heat.

Thus the

ratio l/A is indication of the resistance to the water current in that

part

of the circuit, and we define it, when multiplied by a definite

constant

coefficient c, as "resistance" in a water circuit indicating it by R.

Therefore, we showed if the current (I) was constant (which this

occurred

when the resistances were in series), then the potential difference

between

the two ends of a resistance (V) would be proportional to the

resistance

(R=cl/A).

Now consider some part of the circuit as shown in Fig. 4.

---------------------------------

. . . . . . . . . . . . . . . . .

. . . . . . . . r. . . . . . . .

. . __________________________. .

. .|__________________________| .

. . . . . . . . q. . . . . . . .

. . __________________________. .

. .|__________________________| .

_________________p_______________

Fig. 4. The work performed on a drop being transferred from an end

to the other end is independent of whether the path is p,

q, or r.

The work performed on the drop by the above mentioned force when

passing

this part of the circuit, is independent of the choice of the path p, q

or r, but the water current in these three paths is proportional to

their

cross-sections. As we can see the amount of prevention of p is more

than

of q, and of q is more than of r. Thus the criterion which we obtain in

this

state for the resitance is the same proportion of it to the inverse of

the

cross-section, and since l is the same for the parallel resistances in

this

state, the same definition of R=cl/A is still true for resistance.

Therefore,

we showed if the potential difference (V) was constant (which this

occurred

when the resistances were in parallel), then the current in each

resistance

(I) would be inversely proportional to the resistance (R=cl/A).

Now suppose that the mass of our standard drop is m and suppose that

the

opposing force (of the other drops on the way in the circuit), which as

we

explained prevent the drop from accelerating, is proportional to the

velocity of the drop with the proportion coefficient -G (it is obvious

that

G is proportional to m, because the bigger the drop, the more the

retarding

force is). In this state supposing that the force exerting on the drop

due

to the pump is F and the speed of the drop is v we have the following

equation of motion:

mdv/dt = F-Gv (1)

When the speed of the drop (ie the speed of the water) has become

constant,

we have dv/dt=0 and consequently v=F/G, ie v is proportional to F, and

since

in a constant resistance, v is proportional to I and F is proportional

to V,

we conclude that if the resistance (R) is constant then the current (I)

will

be proportional to the potential (V).

In summary, we showed," If I is constant, then R will be proportional

to V,

and if V is constant, then R will be proportional to 1/I, and if R is

constant, then I will be proportional to V ". We conclude from these

three

deductions that R is proportional to V/I which is the same famous

relation

of Ohm's law in the ohmic electric circuits.

Here it is opportune to obtain the complete solution of the equation

(1).

This will be v(t)=(1/G)F(1-exp(-Gt/m)) if the initial condition is

v[0]=0.

Therefore, the relaxation time is <tau>=m/G. Since as we said G is

proportional to m, the relaxation time <tau> is independent of m.

Likewise,

since the above mentioned force F exerted on the mass m (arising from

the

pump) is obviously proportional to the mass m, the final speed of the

drop

v=F/G, in which both F and G are proportional to m, is also independent

of m.

In other words both the relaxation time, ie the time that the water

speed

requires to reach its constant limit (see the beginning of this

article),

and the final speed of the current, as it is expected, are independent

of

what the bigness or mass of our standard drop is.

As it is quite obvious there is a thorough similarity between the above

water circuit and an electric closed circuit in which the one coulomb

unit

charge plays the role of the above mentioned standard drop, and in fact

in electric circuits a quite similar event occurs, not as it is

supposed

at present an electrostatic field in the wires of the circuit arising

from

the battery causes flowing of the electric current in the electric

circuit!

The only role of the power supply, eg the battery, (similar to the role

of

the water pump) is putting into circulation the current of valence

electrons

of the wires using chemical reactions or electromagnetic effects or

....,

and nothing else; not producing electrostatic field which necessitates

existence of electric net charge assembly which really does not exist.

The fact is that it is thought erroneously that wherever there exist

electric conduction current (I) and potential difference (V), they

should

have been produced because of the existence of some electrostatic field

there, while this is not the case for the electric current flowed by a

power

supply, eg a battery, in a closed circuit, but, quite like in the above

mentioned water circuit, this is only transferring of the force exerted

on

the electrons in the battery (or in other power supplies) which causes

their motion throughout the closed circuit, not existence of any

electrostatic field in the wires. Besides, the potential difference,

by which we mean the amount of work performed on one coulomb of

electric

charge (or on a standard drop) when being transferred from one point to

another point, is not produced necessarily because of an electrostatic

field,

but as we saw the above mentioned forces exerted by the battery and

transferred through the train of electrons can produce it.

For better understanding of the above material, actuality of conduction

has been presented in a simple manner in the 12th article of this book.

Attention to this point is also interesting that as we reasoned

beforehand

(when discussing the complete solution of Equation (1)), the relaxation

time

<tau> and the final speed v, both of the standard charge, are

independent

of the mass (and also of the charge) of the (standard) charge chosen as

the unit charge (and then eg contrary to what is current do not depend

on

the mass or charge of the electron), and only depend on the kind of the

conductor, because G depends on it.

Now let's see whether really the linear relation ~J=g~E is satisfied or

not

when the electrostatic field ~E is exerted in an ohmic conductor

causing

production of temporary current density ~J (which eventually leads to

proper distribution of charge in this conductor such that the field

will

vanish inside it being normal to its surface on its surface). Consider

a

point inside the conductor in a time when the electrostatic field has

not

been exerted yet. The valence electrons are stationing themselves

beside

their atoms. Now consider the moment that an electrostatic field is

exerted

in this point. Certainly this is not the case that immediately after

exertion

of the field in this point, without elapsing any time, current density

~J

becomes flowing in this point. It is quite obvious that a time interval

is

necessary for the valence electrons to separate from their atoms and

becoming flowing produce the current density. Just at the beginning of

this

interval, while there exists the field ~E in this point, there is no

current

there (ie ~J is zero). After elapsing a fraction of the mentioned time

interval, some current becomes flowing (ie ~J reaches a fraction of its

maximum), and since this very amount of current accomplishes a fraction

of

the final distribution of charge (which will make the field vanish

inside

the conductor), the field ~E is also decreased becoming less than its

maximum (approaching zero). This process continues until when the

current

reaches its maximum which is simultaneous with a more decreased field.

After then both ~E and ~J will be decreased approaching zero.

In summary we can see the process of the simultaneous changes of ~E and

~J

schematically in Fig. 5.

A

| A

| | A

| | | A

| | | | A

~E | | | | | .

A A

A | | A

~J . | | | | .

Fig. 5. Schematic diagram of the simultaneous time-changes of ~J and

~E.

What can be deduced definitely is that ~E and ~J don't have any linear

relation in the form of ~J=g~E with the constant coefficient g, even

for

the ohmic mediums.

III. Whether alternating current is not steady

----------------------------------------------

We have the equation of continuity <round><rho>/<round>t+<del>.~J=0.

Steady

current is a current in which, passing the time, concentration of

charge in

each point does not alter, or in other words the charge is not

condensible or

expansible, and then it is necessary that <round><rho>/<round>t to be

zero

for steady currents which according to the equation of continuity it is

also

necessary that <del>.~J=0 for these currents. But we should notice that

in

a steady current it is not necessary that the current has also a

particular

form, ie it is not necessary that <round>~J/<round>t=~0 for a steady

current.

Unfortunately this matter is not observed in many of the textbooks and

circuits carrying steady currents are considered equivalent to direct

current

circuits with this wrong conception that alternating currents are not

steady,

while according to the above-mentioned point although in an alternating

current circuit <round>~J/<round>t is not ~0, the alternating current

is

certainly steady, because in a closed circuit, including the power

supply,

carrying an alternating current, valence electrons of the circuit

itself

(not the external electrons added to the circuit) only alternately

change

direction of their circulation in the circuit, while, passing the time,

the

charge density is constant (and in fact equal to zero) in each point.

The

situation is quite like a closed tube full of water which its water is

oscillating in the tube because of the alternating change in the

direction

of pumping the water by a pump installed in the tube as a part of it.

IV. Resistance due to the configuration of the circuit

------------------------------------------------------

We intend to prove the existence of another kind of electrical

resistance.

This resistance is arising from the form of the current path.

Current-carrying electrons are compelled to move within the boundaries

of

the current-carrying wire in order to cause the electric current. Thus,

naturally, the form, or in other words, the configuration of the

current path

can cause a resistance on the path of the current that is other than

Ohm's

resistance, discussed above, arising from the nature of the current

path

(wire). The cause of this resistance is the mechanical stresses due to

the

collisions of the electrons with the materials of the current path and

their

pressures against these materials (the amount of which depends on the

form

of the current path). The situation is similar to the familiar case of

a

conductor having an excess electric charge: in this state the charge

will

be gathered on the external surface of the conductor and will exert an

outward normal force (or an outward pressure) on the surface that (this

force or pressure) will be canceled out by the mechanical stresses of

the

material of the (surface of the) conductor.

Attention to the following example will clarify the issue. Consider a

part of

a current-carrying wire (from a circuit) (Fig. 6(a)). (Suppose that the

arrow

shows the direction of the motion of the electrons.) Make a loop from

this

part as shown in Fig. 6(b) such that firstly the part ab of the path of

"going" (related to the left (entrance) branch) of the loop and the

part

ab of the path of "backing" (related to the right (exit) branch) of the

loop are very close together but without any contact (at present), and

secondly these two parts of the "going" and "backing" paths (ie ab's)

are

quite parallel to each other.

___________________________________________________________________

( ) -----------------> )

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

(a)

____ ...... ____

_-'`` <----- ``'-_

./` _,--''''''''''''--,_ `\.

/ /' `\ \

,` /` `\ `,

| | | |

` \ / '

`\ `\. ./' /`

_____`-____`_-_.________ ..--'` _-`_____

( ) -----> __,-' -----> )

^^^^^^^^^^^^^^^^^^^^^^^^^````^^^^^^^^^^^^^

a b

(b)

Fig. 6. The current-carrying looped wire makes

the electron move in the loop.

It is obvious that the current in the part ab of each of the "going"

and

"backing" paths is still from left to right having the same amount of

the

circuit current.

Now let's make these two parts (ab's) in (gentle) contact with each

other.

What is the situation of the current in this double part of ab now? If

the

(above-mentioned) resistance arising from the configuration of the wire

did not exist, the most correct answer would be that we should not

expect

any alteration and as the path of the current would have become double

in

the distance between a and b (being both the "going" and "backing"

paths)

the current would be two times more than the general current of the

circuit

(becasuse of the general current of the circuit both in the "going" and

"backing" paths of ab). But certainly this is not the case completely,

and

due to the contact of the two "going" and "backing" parts of ab a part

of

the previously mentioned stresses will be redistributed (trying to

become

minimum) and then the above-mentioned resistance, arising from the

configuration, will change and then the current in the loop and also in

the common part of ab will be other than the case before the contact;

the

quite clear reason for this statement is that when the two parts of ab

are

in contact we expect in principle that because of the positioning of a

before b the current in the loop to be counterclockwise (from a to b)

not

clockwise (from b to a) as before the contact.

Now imagine that these parts of ab are welded together, and in the

distance

between a and b we have only a single wire with a thickness equal to

the

wire thickness in other parts of the circuit (and loop). In this state

if we

want to visualise the situation just before the contact of the two

"going"

and "backing" parts of ab as one we explained above, we must say that

before

the above-mentioned gentle contact the cross-section of the circuit in

the

"going" part of ab and also in the "backing" part of ab is half of the

cross-section in other parts of the circuit, then the speed of the

electrons

in each of the two "going" and "backing" parts of ab is twice as more

as the

electrons speed in other parts of the circuit. Now, if these two

slenderized

"going" and "backing" parts of ab are to be brought into contact with

each other (welded together) and also if the currents are not to be

changed,

the situation will be as shown in Fig. 7, ie as we see in this figure,

according to the above reasoning assuming ineffectiveness of the

configuration on how the current is distributed, we expect that the

current

in the part ab of the circuit to be twice as more as the general

current of

the circuit halh of which, of course, will be canceled as the "backing"

(counterclockwise) current in the loop.

_.,--''''''''''''''''''''--,._

_,-' <----- `-,_

/ _.--'''``````````````'''--._ \

,` /` `\ ',

| | | |

`, \_ _/ ,`

\ `'--..,______________,..--'` /

`'-,__ -----> __,-'`

/^\^^^^^^^^^^^^` -----> `^^^^^^^^^^^^\

\ / -----> _,--'``````````````'--,_ -----> /

```````````````` a b ``````````````

Fig. 7. What is the situation of current in the part ab and in the

loop?

It is obvious of course that this won't be the case in practice,

because,

as a rule, as we said, we expect in principle that because of the

positioning

of the point a before b in the current path the current in the loop to

be

(clockwise) from a to b.

The conclusion we can decisively draw is that, anyway, the inclination

existent in the circuit to produce a counterclockwise current in the

loop before the contact of the two previously separated parts of ab,

now after the contact (or welding of the two parts), depending on the

configuration of the current-carrying wire of the loop relative to the

configuration of the main wire of the circuit, will have a noticeable

effect

on the current which as a rule is expected to be clockwise in the loop

(because of the point a being before b); and, in practice, the current

in the

loop may be even counterclockwise, even with little current, depending

on

the case; ie in other words we can have a negative resistance (of the

configuration kind) causing the current in the part between a and b to

be

more than the general current of the circuit. We have pointed to such a

case

in the 8th article of this book. We can also try the experiment

suggested

in Fig. 8 in order to see whether the current in the loop is clockwise

or

counterclockwise, and with what current.

____________________

_-'`` ``'-_

./` _,--''''''''''''''''''--,_ `\.

/ /' `\ \

,` /` `\ `,

| | | |

` \ / `

`\ `\. ./` /`

__________-. ``--..______________..--`` _-`

----> __,-'

^^^^^^^^^^^^^^^^^^^^^^^^^| |^^^^^````

a | |b

| |

| |

| |

| |

Fig. 8. Is the current in the loop clockwise or counterclockwise?

V. Action mechanism of transistor

---------------------------------

As a general confirmation of the mechanism presented in this article

for

the resistance arising from the configuration of the current path and

also

of the validity of the comparison made between the electric current and

water current we shall proceed to describe the action mechanism of

transistor in this section.

We know that some different materials gather electrostatic charge when

robbed with each other. Consider two typical materials of this kind and

call them 1 and 2. Assume that some electrons will flow from 1 to 2

when

they are brought into contact. Important for us in this discussion is

the

tendency (due to any reason, eg the molecular structure of the

materials)

existent in the contact between 1 and 2 to cause the electrons to flow

from 1 to 2.

Now let's connect the negative pole of a battery to 1 and its positive

pole to 2. The battery tends to make the electrons flow from its

negative

pole to its positive pole in a circuit external to the battery a part

of

which is the battery itself. Such a flow will be from 1 to 2

considering

the above-mentioned connecting manner. But as we said, regardless of

the

stimulation of the battery, the materials 1 and 2 themselves have a

tendency to establish an electron current from 1 to 2. Thus, it is

obvious

that the battery will establish a current of electrons, from 1 to 2, in

the circuit without encountering much resistance (due to the junction

1-2).

But when the negative pole of the battery is connected to 2 and its

positive

pole is connected to 1, the battery as before wants to produce a

current of

electrons from its negative pole to its positive pole in the circuit a

part

of which is the battery itself, and this necessitates flow of electrons

from 2 to 1 which is opposite to the natural tendency of the junction

1-2;

thus, the electron current of the circuit will encounter much

resistance

at the junction 1-2. In other words for prevailing over this additional

resistance in order to have a current with the same intensity as before

in the circuit it is necessary to use a battery with a higher voltage.

Let's show the tendency of a junction to establish a current of

electrons

by an arrow in the direction of this tendency. Suppose that we have two

adjacent junctions of the above-mentioned type (having natural tendency

to make the electrons flow) but with two opposite directions of

tendency

in a single block; see Fig. 9. We name such a block as transistor.

<== ==> ==> <==

_________________________ _________________________

| | | | | | | |

| | | | | | | |

| | | | | | | |

| 1 | 2 | 3 | or | 1 | 2 | 3 |

| | | | | | | |

| | | | | | | |

| | | | | | | |

^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^

(a) (b)

Fig. 9. Two types of transistor.

Let's construct a circuit as shown in Fig. 10 using a transitor of the

type (a) in Fig. 9, two batteries, some connecting wires and an on/off

switch.

==> <==

_________________________

| | | |

| | | |

| | | |

,---------------| 1 | 2 | 3 |---------------,

| | | | | |

| | | | | |

| | | | | |

\ ^^^^^^^^^^^^|^^^^^^^^^^^^ |

`\. a | b |

| | |

| | |

| | | | |

'--------| |----------------'------------| ... |--------'

| c |

- + - +

Fig. 10. A typical circuit of a transistor of the type (a) in Fig.

9.

When the switch is off we have only a weak clockwise current of

electrons

in the right loop. When the switch if on the clockwise electron current

in the left loop begins and increases until the current has such an

intensity that causes some part of the current previously flowed in the

middle wire to be exerted on (ie to flow in) the right loop through the

junction 2-3 causing increase in the weak current of electrons in this

loop.

And this will be more effective when the material 2 is thinner and

wider

because in such a case the electrons passing through the junction 1-2

will be exerted on (or will be forced onto) the junction 2-3 more

readily

and more effectively.

If we construct the circuit of Fig. 11 using a transistor of the type

(b)

in Fig. 9, we shall observe that while the switch being off there will

be

only a weak counterclockwise current of electrons in the right loop.

<== ==>

_________________________

| | | |

| | | |

| | | |

,---------------| 1 | 2 | 3 |---------------,

| | | | | |

| | | | | |

| | | | | |

\ ^^^^^^^^^^^^|^^^^^^^^^^^^ |

`\. a | b |

| | |

| | |

| | | | |

'--------| |----------------'------------| ... |--------'

| c |

+ - + -

Fig. 11. A typical circuit of a transistor of the type (b) in Fig.

9.

And when the switch is on a counterclockwise current of electrons will

begin and increase in the left loop. This current will become such

intense

that eventually a part of the electron current, previously flowed in

the

middle wire at the point c towards 2, now will be exerted on (or will

go into) the right loop causing increase in the weak counterclockwise

current of electrons in this loop. This will be more effective when the

material 2 is thinner and wider because in such a case the electrons

passing through the junction 3-2 will be exerted on (or will be forced

onto) the junction 2-1 more readily and more effectively (causing

increase

in the electron current passing through the left battery which

eventually

will cause more increase in the electron current passing through the

right battery).

Now imagine such an ideal state of the figures 10 and 11 (with switches

being on) that the magnitudes of the upward and downward currents in

the

middle wire are the same and then these currents cancel each other.

In such a state that there is no current in this wire (and a

considerable

current in the whole circuit) we can eliminate this wire from the whole

circuit in principle. But, could we do this before switching on the

switch?

It seems that the answer is negative and the current in a circuit

without

the middle wire cannot increase to the extent accessible by a circuit

with

the middle wire (while the switch being on). If so, we have presented a

practical (or experimental) confirmation of the starter mechanism (ie

the

first current in a loop that increases and eventually causes increase

in

the current in the other loop due to the exertion of the current

pressure).

We can introduce for a transistor too a mechanical (or hydrodynamical)

analogue which itself helps to understand the action mechanism of

transistor better. Let's construct it as shown in Fig. 12.

___________________________________________________

| * * |

| | | |

| ' ' |

| * * |

_____| | | |_____

' '

* *

^^^^^| | | |^^^^^

| ' ' |

| * * |

| | | |

| ' ' |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A B

Fig. 12. A hydrotransistor

In this figure some hinged blades are set up one after the other in two

adjacent surfaces A and B as their cross-section is shown in Fig. 12.

Suppose that in one type of the above-mentioned hydrotransistor the

blades

of the surface A can be opened readily towards B and the blades of B

can

be opened readily towards A (Fig. 13(a)) while the blades of each

surface

can be opened towards the opposite side hardly (Fig. 13(b)), and in the

other type the blades of each surface can be opened readily towards the

side opposite to one in which the other surface is located while being

able to be opened towards the other surface hardly (Fig. 14).

___________________________________________________

| *---- ----* |

| |

| |

| *---- ----* |

_____| |_____

*---- ----*

^^^^^| |^^^^^

| |

| *---- ----* |

| |

| |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A B

(a)

___________________________________________________

| * * |

| /` `\ |

| ` ` |

| * * |

_____| /` `\ |_____

` `

* *

^^^^^| /` `\ |^^^^^

| ` ` |

| * * |

| /` `\ |

| ` ` |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A B

(b)

Fig. 13. How a hydrotransistor of a type works.

___________________________________________________

| ----* *---- |

| |

| |

| ----* *---- |

_____| |_____

----* *----

^^^^^| |^^^^^

| |

| ----* *---- |

| |

| |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A B

(a)

___________________________________________________

| * * |

| `\ /` |

| ` ` |

| * * |

_____| `\ /` |_____

` `

* *

^^^^^| `\ /` |^^^^^

| ` ` |

| * * |

| `\ /` |

| ` ` |

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A B

(b)

Fig. 14. How a hydrotransistor of the other type works.

Let's construct the hydrocircuit of Fig. 15 using the hydrotransistor

of

the type shown in Fig. 13.

___________________________________________________

| *---- * |

| `\ |

| ` |

| *---- * |

_________| `\ |_________

| ` |

| *---- * |

| |^^| `\ |^^| |

| | | ` | | |

| | | *---- * | | |

| | | `\ | | |

| | | ` | | |

| | ^^^^^^^^^^^^^^^^^^^^^^^| |^^^^^^^^^^^^^^^^^^^^^^^ | |

| __|__() v A | | B ,--> | |

| ^^|^^() ,-> | | /` _____ | |

| | /` .,-,. | | ` /' ; '\ | |

| | /` | `\ | |_______/` | `\_____| |

| ^^^^^^^^^` ---*--- `^^^^^^^ ----*---- |

| | | |

'-------------------------------------------------'-----------------'

a b

Fig. 15. A hydrocircuit containing a hydrotransistor.

When the valve is off and the pumps a and b are on we have only a slow

clockwise water current in the right loop. But when the valve is on the

clockwise water current will begin in the left loop and will be

accelerated

gradually and little by little the water will gain such (kinetic)

energy

that the blades of A will be opened completely and the accelerated and

energetic water will force itself onto the blades of B too, causing

them

to be opened more and to let more water pass into the right loop and

circulate clockwise. A hydrocircuit containing a hydrotransistor of

the

other type will have a function similar to what we explained previously

about the electric transistor analogou with it.

Now suppose that the hydrocircuit shown in Fig. 15 have no middle tube.

In such a case is it possible for the water to be accelerated gradually

after switching the valve on until the same intensity of current is

obtained that would be obtained if the middle tube existed? The answer

is negative because when there is no middle tube the weak (or slow)

clockwise water current produced in the circuit will soon reach an

equilibrium state in which both the current intensity of the circuit

and

the amount of opening of the blades of B will remain constant on some

small values. (The situation is quite similar to the right single loop

of Fig. 15 itself in which there will be a small constant clockwise

current in the loop corresponding to a small opening of the blades of B

when the valve is switched off.) But the existence of the middle tube

and

the above mentioned mechanism cause the clockwise water current of the

left loop to gain (kinetic) energy as much as possible and then to rush

onto the blades of B opening them noticeably with its huge energy.

Hamid V. Ansari

My email address: ansari18109<at>yahoo<dot>com

The contents of the book "Great mistakes of the physicists":

0 Physics without Modern Physics

1 Geomagnetic field reason

2 Compton effect is a Doppler effect

3 Deviation of light by Sun is optical

4 Stellar aberration with ether drag

5 Stern-Gerlach experiment is not quantized

6 Electrostatics mistakes; Capacitance independence from dielectric

7 Surface tension theory; Glaring mistakes

8 Logical justification of the Hall effect

9 Actuality of the electric current

10 Photoelectric effect is not quantized

11 Wrong construing of the Boltzmann factor; E=h<nu> is wrong

12 Wavy behavior of electron beams is classical

13 Electromagnetic theory without relativity

14 Cylindrical wave, wave equation, and mistakes

15 Definitions of mass and force; A critique

16 Franck-Hertz experiment is not quantized

17 A wave-based polishing theory

18 What the electric conductor is

19 Why torque on stationary bodies is zero

A1 Solution to four-color problem

A2 A proof for Goldbach's conjecture