Geometrical Resistance
Geometric Resistance
It has occured to me that its worth mentioning the importance of the geometrical
dimensions of wires and coils, as it relates to Resistance, Amperes, Volt and Magnetic fields.
How can Ohms Resistance be geometric one might ask.
I can say so by describing it with an example.
I have a cube of copper that is 1 cm in every dimension. X, Y and Z. That represent lenght, width and tallness and equalling 1 cubic centimeter. When I put the multimeter electrodes onto that coppercube and measure the Resistance, the value is very low, maybe 0.0001 Ohm.
If one retains the wheight of that 1 cubical centimeterm of copper that is 8.9 grams and forge it into a wire, that is 10 - 15 meters long and a diameter of 0.511 mm, AWG#24 wire. When measuring the Resistance of the complete wire lenght from end to end, the Resistance has increased ! Altough the "mass" in kilograms that actually states the number of atoms, is the same in both instances. The resistance has increased from maybe 0.001 to 0.1 Ohm . This implies that less Amperes is conducted through the wire of AWG#24 than a cubic cm, although they have the same amount of atoms inside them. When the Voltage is kept the same level in both instances.
How can this be ?
The thinner and longer the wire is, the larger the Voltage
is needed to penetrate the wires Resistance, so Amperes can be conducted through the wire.
And create what we expect from electrical energy, heat (Celcius), magnetic fields (B-fields)
and static (E-fields).
Again, by even further decreasing the diameter from 0.511mm AWG#24 into 0.13mm AWG#36 and
keeping the same wheight of wire at 8.9 grams. That will result in a wire several hundred meters long, with a tremendous Resistance. maybe over 2-300 Ohms ! But still, the same wheight as the copper cube of 1 cm^3.
One might ask, why is that interesting ?
well, because the amount of Voltage needed to penetrate the wire is of concerne, due to the amount of Amperes the wire can handle before it heats too much and burns off like a fuse, or create short circuits.
A slim wire of AWG#36 that is 0.13 mm thick, is about the thickness of a hair.
By driving 230V household mains through that wire would require a very long
wire to increase the Resistance, so it does not burn off in an instant. Then the Voltage is dropped, the Resistance is high. The Ampere is lowered to keep the temprature down on the wire, so it doesnt overheat. The wire is therefore a load on itsown. Not just the Lamp, the stove heater, the TV or transformer, but the wire is also a load.
Since the Ampere in the wire is directly transferrable
to the magnetic field., and also directly transferrable to temprature heat. a wire with large Resistance and low Ampere, also has a smaller magnetic field. The number of turns is increased, to increase the magnetic field.
Now the wire in a coil, that is the central component in transformers and the unit that concentrates and focus the magnetic field into a small area. When a wire is stretched out in a distance, a so called - a lone wire. The magnetic field is running along the wire and the concntration of the magnetic field is at its weakest concentration. By coiling the wire into several turns that adds upon one another the concentration of the magnetic field increase, and so does the heat temprature. One can therefore design the coil with a given wheight of copper, to a given source of voltage potential, to behave at an optimal magnetic field, without overheating. Be it AC or DC. the DC coil will have constant heat through its wires and will not be allowed to "relax or cool down". the AC coil is for each period passing 0 volts, so it may cool during operation.
When turns are packed tight and a large Ampere is running through, it is of critical importance to figure out how many Amperes that can run through the wire witout overheating the wire so it shortcircuits.
One usually design the coil to fit the potential of the source, A 12 volt battery, or 230 V mains. The Amperes is usually given by the amount of parallell plates in the battery, or "sourness" of the electron donor or acid. Some trailer truck batterys have up to 150 Amperes. A house hold mains 230V, usually allows 16A or 25 Amperes. If there was no fuses a short circuit would consume the complete power grid ! Practially the smallest crossection wire would break the connection.
Concerning the heat in a coil
Heat convection, is when heat from several turns is transferred to the neighbouring turns of wire.
A wire that is enclosed by many other turns will certainly be hotter than a wire wire on the outer layer of a coil. or a lone wire by itself in a cool environment, like them superconductors in cryogenic freeze.
When having coils with iron core. Once the iron gets hot it takes "long time" before it cools down.
A coil of AWG24 with 200 turns and 3 amperes DC, and and Iron core
once the core is hot it takes atleast 30- 40 minutes before it cools down and can be toutched with human hands. With only 3 amperes such a coil is bound to melt the insulation and break down.
Instances of Reactance in AC, relating to Geometry of the conductor.
When the current is alternating, complex numbers calculated in well known triangles of Pythagoreas is sorted to in the "Reseistance triangle". In this triangle the Horizontal line is Resistive load like DC applications, heaters and lamps. The diagonal line is Impedance and the combination of Resistive and Reactive or Inductive load, The Vertical line describe this phenomena known as Reactance also known as eddy currents, facault currents or self induction. That is visualized by small "tornadoes" currents that subtract
the incoming halfwave with the previos wave valley of the opposite polarity and direction. This tornado shape is also appearing in water Drains in bathtubs. And equal to the word, it "drains" electrical power .
It is visualized as dragging an ore of a boatsman, with the broadside ore through the water.
Then small swirls are seen in the water. These subtract the alteration of current and drain the effect. The
similarities with water and electricity is described down the text.
This results in a wire of relative small resistive Ohmic value, can have enormous Reactive Resistance
if the self inducton is large. That is the "convection"of magnetic field is large. If I may use the word
of heat convection or transferring Heat onto the neighbouring turns, also the Magnetic field induce onto the neighboring turns, and can analogly be understood as "magnetic convection". Described in the unit L = Henrys. A coil of large Ampere will therefore subtract much of its own circulating Ampere by " Magnetic convection" or Self Induction. As the frequency increase the Reactance also increase.
Anyways by altering the geomtery of the coil the Reactance can also be changed, by increasing the distance between the turns. Also choosing the correct thickness of insulation the Capacitive properties can be
designed for optimal use. Since the Electrostatical E-field is stored on the insulation, a proper design removes the need of an external capacitor. But would on the other hand be fixated to one type of frequency, Voltage and Ampere. Because all these parameters will be altered, if one of them are changed indevidually.
Even the Resistance changes with Voltage and Amperes. Because the Heat of a wire, increase the Resistance.
Every electrical component is therefor in varying degrees, a conductor, resistor, capacitor, and inductor. What is understood as an electrical component is every atomic number in the periodical system,, because all Atoms and Molecules in Nature have Electrical properties. the Electron being a subatomic particle of negative charge. The Proton or atomic core, forming the nucleus UUD, is positive. And therefore of electrostatic nature.
See that water and electricity is very much the same. the voltage is understood as the pressure of water through a pipe. The water is the Ampere or Electrons in motion through the pipe.
The Voltage can also be a basin that can collect rain water at an elevated place, like between tall mountains. There fore called correctly Potential energy. Ampere on the other hand is in motion and Kinetic, it moves
so it is rather : cinematic. Kino, is the same word as cinema ... both mean motion, Kinetic.
High Voltage equals Large pressure, and can motivate Amperes through
a long pipe or long distance transmission cables, that has large Resistance. Rather, the pipe and conductor alike consumes much energy due to friction of the kinetic mass (Amperes or water).
The pressure and amount of water in parallell divided pipe system would also be analog to Parallell coppled circuits described by Kirchoffs in his formula. Kirchoffs formula would be equally usable in both water pipes as in electrical circuits, in my understanding. Pipes with loads in series equal to serie coppled wires,
the pressure is dropped, the longer the pipe, or narrower the diameter of the pipe. Describing the Volt drop in serie coppled loads, like a christmas lights arrangement.
Also surprisingly enough in Watt transformation the water analogy is yelding. See a garden hose with water. The pressure of the water can be low, resulting in a slack (parabolic shaped) bow of the water, but a large amount of water sprouts out when the nozzle is of wide diameter. By squeezing the nozzle tight, the pressure increase in the water hose, and the amount of water escaping the nozzel decrease. Now, what happens is that with a tight nozzle the water can sprout very far, 3, 4, 5 times the distance as before. That is exactly the same in transformation from High Ampere and low Voltage at the generator and domestic use,
into ( high Impedance watt ). that is High Voltage and low Ampere used specifically for transmission of power over large distances. Or in my own terminlogy from Warm, low impedance watt, into Cold Watt of high Impedance. The Watt product is consistant, but the energy "vectors, Volt and Ampere" is transforming values.
Now the geometry of a coil is of great complexity and very interesting. lets say I have 10 meter of wire in 1 turn. Tthe Amperic field or rather Magnetic field around the wire may be extending 1 mm, at 1 Ampere from the surface of the conductor wire. By coiling the wire 2 turns, and thus obtaining half the radial distance of the core. That 1 ampere adds up and the Magnetic field is focused into a more narrow areal. Not
infintly small, because that is physically impossible for anything real (material) like a copper wire to be wined in smaller turns, than the diameter of the wire. In short, the design of the Magnetic field in a coil is also geometrical. Because the Radius of the core, determine the area of Magnetic action.
And the amount of Ampere, in each turn also increase the Magnetic field affecting the temprature. Interestingly the increase of turns, also increase the Reactance Resistance, and will actually decrease the Ampere in the coil. therefore the term "choke coil" in antennas, and Radio circuits. The Voltage on the other hand is linear to the velocity of the frequency, and amount of turns.
Volt, Ampere, Resistance and Magnetic fields, in circuit with a electrical source Battery
or Alternating Generator the electrical result part is geometrical, part atomic material properties.
Conclusion is therefore. When changing the geometric properties of the wire, one
also varys the parameter of Volt ( needed to penetrate the wire, break down the Resistance ).
Ampere ( size, volum or strenght of the Magnetic field and also the temprature heat, of the wire).
And Resistance in electrical conductors. By retaining the same atomic mass in kilograms, but altering the geometrical form of the conductor.
And thats it for today .
Kenneth
NB. the exact numbers are just examples in this text.
It has occured to me that its worth mentioning the importance of the geometrical
dimensions of wires and coils, as it relates to Resistance, Amperes, Volt and Magnetic fields.
How can Ohms Resistance be geometric one might ask.
I can say so by describing it with an example.
I have a cube of copper that is 1 cm in every dimension. X, Y and Z. That represent lenght, width and tallness and equalling 1 cubic centimeter. When I put the multimeter electrodes onto that coppercube and measure the Resistance, the value is very low, maybe 0.0001 Ohm.
If one retains the wheight of that 1 cubical centimeterm of copper that is 8.9 grams and forge it into a wire, that is 10 - 15 meters long and a diameter of 0.511 mm, AWG#24 wire. When measuring the Resistance of the complete wire lenght from end to end, the Resistance has increased ! Altough the "mass" in kilograms that actually states the number of atoms, is the same in both instances. The resistance has increased from maybe 0.001 to 0.1 Ohm . This implies that less Amperes is conducted through the wire of AWG#24 than a cubic cm, although they have the same amount of atoms inside them. When the Voltage is kept the same level in both instances.
How can this be ?
The thinner and longer the wire is, the larger the Voltage
is needed to penetrate the wires Resistance, so Amperes can be conducted through the wire.
And create what we expect from electrical energy, heat (Celcius), magnetic fields (B-fields)
and static (E-fields).
Again, by even further decreasing the diameter from 0.511mm AWG#24 into 0.13mm AWG#36 and
keeping the same wheight of wire at 8.9 grams. That will result in a wire several hundred meters long, with a tremendous Resistance. maybe over 2-300 Ohms ! But still, the same wheight as the copper cube of 1 cm^3.
One might ask, why is that interesting ?
well, because the amount of Voltage needed to penetrate the wire is of concerne, due to the amount of Amperes the wire can handle before it heats too much and burns off like a fuse, or create short circuits.
A slim wire of AWG#36 that is 0.13 mm thick, is about the thickness of a hair.
By driving 230V household mains through that wire would require a very long
wire to increase the Resistance, so it does not burn off in an instant. Then the Voltage is dropped, the Resistance is high. The Ampere is lowered to keep the temprature down on the wire, so it doesnt overheat. The wire is therefore a load on itsown. Not just the Lamp, the stove heater, the TV or transformer, but the wire is also a load.
Since the Ampere in the wire is directly transferrable
to the magnetic field., and also directly transferrable to temprature heat. a wire with large Resistance and low Ampere, also has a smaller magnetic field. The number of turns is increased, to increase the magnetic field.
Now the wire in a coil, that is the central component in transformers and the unit that concentrates and focus the magnetic field into a small area. When a wire is stretched out in a distance, a so called - a lone wire. The magnetic field is running along the wire and the concntration of the magnetic field is at its weakest concentration. By coiling the wire into several turns that adds upon one another the concentration of the magnetic field increase, and so does the heat temprature. One can therefore design the coil with a given wheight of copper, to a given source of voltage potential, to behave at an optimal magnetic field, without overheating. Be it AC or DC. the DC coil will have constant heat through its wires and will not be allowed to "relax or cool down". the AC coil is for each period passing 0 volts, so it may cool during operation.
When turns are packed tight and a large Ampere is running through, it is of critical importance to figure out how many Amperes that can run through the wire witout overheating the wire so it shortcircuits.
One usually design the coil to fit the potential of the source, A 12 volt battery, or 230 V mains. The Amperes is usually given by the amount of parallell plates in the battery, or "sourness" of the electron donor or acid. Some trailer truck batterys have up to 150 Amperes. A house hold mains 230V, usually allows 16A or 25 Amperes. If there was no fuses a short circuit would consume the complete power grid ! Practially the smallest crossection wire would break the connection.
Concerning the heat in a coil
Heat convection, is when heat from several turns is transferred to the neighbouring turns of wire.
A wire that is enclosed by many other turns will certainly be hotter than a wire wire on the outer layer of a coil. or a lone wire by itself in a cool environment, like them superconductors in cryogenic freeze.
When having coils with iron core. Once the iron gets hot it takes "long time" before it cools down.
A coil of AWG24 with 200 turns and 3 amperes DC, and and Iron core
once the core is hot it takes atleast 30- 40 minutes before it cools down and can be toutched with human hands. With only 3 amperes such a coil is bound to melt the insulation and break down.
Instances of Reactance in AC, relating to Geometry of the conductor.
When the current is alternating, complex numbers calculated in well known triangles of Pythagoreas is sorted to in the "Reseistance triangle". In this triangle the Horizontal line is Resistive load like DC applications, heaters and lamps. The diagonal line is Impedance and the combination of Resistive and Reactive or Inductive load, The Vertical line describe this phenomena known as Reactance also known as eddy currents, facault currents or self induction. That is visualized by small "tornadoes" currents that subtract
the incoming halfwave with the previos wave valley of the opposite polarity and direction. This tornado shape is also appearing in water Drains in bathtubs. And equal to the word, it "drains" electrical power .
It is visualized as dragging an ore of a boatsman, with the broadside ore through the water.
Then small swirls are seen in the water. These subtract the alteration of current and drain the effect. The
similarities with water and electricity is described down the text.
This results in a wire of relative small resistive Ohmic value, can have enormous Reactive Resistance
if the self inducton is large. That is the "convection"of magnetic field is large. If I may use the word
of heat convection or transferring Heat onto the neighbouring turns, also the Magnetic field induce onto the neighboring turns, and can analogly be understood as "magnetic convection". Described in the unit L = Henrys. A coil of large Ampere will therefore subtract much of its own circulating Ampere by " Magnetic convection" or Self Induction. As the frequency increase the Reactance also increase.
Anyways by altering the geomtery of the coil the Reactance can also be changed, by increasing the distance between the turns. Also choosing the correct thickness of insulation the Capacitive properties can be
designed for optimal use. Since the Electrostatical E-field is stored on the insulation, a proper design removes the need of an external capacitor. But would on the other hand be fixated to one type of frequency, Voltage and Ampere. Because all these parameters will be altered, if one of them are changed indevidually.
Even the Resistance changes with Voltage and Amperes. Because the Heat of a wire, increase the Resistance.
Every electrical component is therefor in varying degrees, a conductor, resistor, capacitor, and inductor. What is understood as an electrical component is every atomic number in the periodical system,, because all Atoms and Molecules in Nature have Electrical properties. the Electron being a subatomic particle of negative charge. The Proton or atomic core, forming the nucleus UUD, is positive. And therefore of electrostatic nature.
See that water and electricity is very much the same. the voltage is understood as the pressure of water through a pipe. The water is the Ampere or Electrons in motion through the pipe.
The Voltage can also be a basin that can collect rain water at an elevated place, like between tall mountains. There fore called correctly Potential energy. Ampere on the other hand is in motion and Kinetic, it moves
so it is rather : cinematic. Kino, is the same word as cinema ... both mean motion, Kinetic.
High Voltage equals Large pressure, and can motivate Amperes through
a long pipe or long distance transmission cables, that has large Resistance. Rather, the pipe and conductor alike consumes much energy due to friction of the kinetic mass (Amperes or water).
The pressure and amount of water in parallell divided pipe system would also be analog to Parallell coppled circuits described by Kirchoffs in his formula. Kirchoffs formula would be equally usable in both water pipes as in electrical circuits, in my understanding. Pipes with loads in series equal to serie coppled wires,
the pressure is dropped, the longer the pipe, or narrower the diameter of the pipe. Describing the Volt drop in serie coppled loads, like a christmas lights arrangement.
Also surprisingly enough in Watt transformation the water analogy is yelding. See a garden hose with water. The pressure of the water can be low, resulting in a slack (parabolic shaped) bow of the water, but a large amount of water sprouts out when the nozzle is of wide diameter. By squeezing the nozzle tight, the pressure increase in the water hose, and the amount of water escaping the nozzel decrease. Now, what happens is that with a tight nozzle the water can sprout very far, 3, 4, 5 times the distance as before. That is exactly the same in transformation from High Ampere and low Voltage at the generator and domestic use,
into ( high Impedance watt ). that is High Voltage and low Ampere used specifically for transmission of power over large distances. Or in my own terminlogy from Warm, low impedance watt, into Cold Watt of high Impedance. The Watt product is consistant, but the energy "vectors, Volt and Ampere" is transforming values.
Now the geometry of a coil is of great complexity and very interesting. lets say I have 10 meter of wire in 1 turn. Tthe Amperic field or rather Magnetic field around the wire may be extending 1 mm, at 1 Ampere from the surface of the conductor wire. By coiling the wire 2 turns, and thus obtaining half the radial distance of the core. That 1 ampere adds up and the Magnetic field is focused into a more narrow areal. Not
infintly small, because that is physically impossible for anything real (material) like a copper wire to be wined in smaller turns, than the diameter of the wire. In short, the design of the Magnetic field in a coil is also geometrical. Because the Radius of the core, determine the area of Magnetic action.
And the amount of Ampere, in each turn also increase the Magnetic field affecting the temprature. Interestingly the increase of turns, also increase the Reactance Resistance, and will actually decrease the Ampere in the coil. therefore the term "choke coil" in antennas, and Radio circuits. The Voltage on the other hand is linear to the velocity of the frequency, and amount of turns.
Volt, Ampere, Resistance and Magnetic fields, in circuit with a electrical source Battery
or Alternating Generator the electrical result part is geometrical, part atomic material properties.
Conclusion is therefore. When changing the geometric properties of the wire, one
also varys the parameter of Volt ( needed to penetrate the wire, break down the Resistance ).
Ampere ( size, volum or strenght of the Magnetic field and also the temprature heat, of the wire).
And Resistance in electrical conductors. By retaining the same atomic mass in kilograms, but altering the geometrical form of the conductor.
And thats it for today .
Kenneth
NB. the exact numbers are just examples in this text.
Kommentarer
EDIT : The Voltage on the other hand is linear to the velocity of the Magnets velocity on the generator determining the frequency on the terminals. the Voltage also is seemingly linear to the amount of turns relating to the strenght of magnets projecting onto the stator coils, that pick up the magnetic field from the rotor, and create the resulting Watt of Volt potential and Amperes on the Terminals.