Ohm’s Law for the chain section is the basic formula that teachers use to deal with disobedient students. Let's see what George Om wanted to convey to descendants when he formulated the law:
I = U / R.Where I is the amperage measured in amperes;U is the voltage, in volts;and R is the resistance in ohms.
The history of creation of Ohm's law for a section of a circuit
In combination with the knowledge that the voltage of parallel circuits is the same as the current in series, Ohm's law for a section of a circuit becomes a powerful tool for solving any problems. Being derived in 1827, the formula is several decades ahead of the work of Kirchhoff. Georg Om experimented with active resistances and for two whole years struggled with what today would be enough for an ordinary student for half an hour. All from a lack of material base.
In 1600, Volta presented a battery to the public, the researchers began to look for where to adapt the innovation. It became obvious that it was possible to transmit information quickly and over long distances using a telegraph. But there was nothing to measure. Obviously, no current and voltage are related later by Ohm’s law for a section of the circuit. The difficulty loomed on the horizon only during the period when the need for repairs appeared. After forty years from the birth of Ohm’s law, when the transatlantic telegraph was laid in 1866, the Kelvin mirror galvanometer was used as a receiver.
8 years before this, the future lord took a patent for an invention. In its original form, the device is a coil of wire, with a movable mirror inside. At the moment when the current was recorded in the circuit, the light was reflected in the right direction, the operator saw what was happening with his own eyes. Agree, with the help of such a device is difficult to measure. Kelvin amended, it happened 40 years later than was desirable for George Ohm.
The inventor of the first accurate ammeter, Edward Weston, was born in 1850.The device was manufactured by 1886 and ensured accuracy of 0.5%.Obviously, George Om did not use the device when searching for the law for the chain section. However, brought the famous formula. How? He was known as a magnificent mathematician and in his research he used Fourier's ideas on heat conduction.
The galvanic circuit study mathematically easy to download in pdf format from the Google repository. True, a translation into Russian cannot be found even in the central library of the name of Lenin.
Prehistory of George Ohm's discoveries
Earlier Thales Miletsky was already mentioned in the topics;Humanity in the field of electricity owes much to women and their curiosity, which forced her daughter to ask Papa Thales for an explanation for an incomprehensible phenomenon.
Then the electricity was forgotten for centuries. The first serious work in this area is the work of William Gilbert, shortly before his own death who managed to publish a treatise, the name of which can be freely translated as “About a magnet, magnetic bodies and a large magnet - the Earth”.It is impossible to pass by Otto von Guericke, with the help of a static charge generator of his own design who has managed to establish a number of curious patterns:
- The charges of the same sign are repelled, the opposite are attracted. Von Gerike drew attention to these opposites.
- With the closure of charges of different signs conductor flows current. At that time, no concept existed, but the fact of the disappearance of the interaction forces between the bodies was noticed.
He noted the presence of signs in charges by Charles Dyufé: they already wrote about "glass" and "pitch" electricity.
How Georg Ohm derived the law mathematically
The authors made a small translation of an entire( !) Book on the mathematical study of the electrical circuit. Om writes that labor was created on the basis of only three postulates:
- . The spread of electricity inside a solid body( conductor).
- The movement of electricity outside a solid body( we venture to suggest that we are talking about a magnetic field).
- The phenomenon of the appearance of electricity when dissimilar conductors contact( now called a thermocouple).
The scientist writes that he relied on the air, the last two postulates were not in the form of laws at that time, only partial experimental developments were present. The studies were based on the experiments of Charles Coulomb, who experimented with the actions of charges on each other remotely. Already then, Ohm suggested that two contacting dissimilar conductors form a potential difference. And now Ohm's amazing discoveries:
- As mentioned above, there were no measuring instruments at that time. Om knew from scientific publications that the current flowing through the wire deflects the magnetic needle aside. It was not easy to correlate the angle with the amount of electricity, but the scientist went to the trick: with the help of torsional weights he began to determine the force at which the compass readings and the direction of the metal core coincided. And in Newtons this is an extremely small value. So Om learned to measure exactly the strength of the current - a quantity unknown to the scientific community, introduced into the use of the genius of science.
- During the experiments it was noticed that the volt pole does not give a constant voltage. Experiments in such conditions, George Om could not continue. And he began to use. .. thermo-emf( on the advice of physicist I. H. Poggendorf).This is amazing because low voltages - the potential difference between two dissimilar conductors( copper and bismuth) - cause insignificant currents. Om coped with the task with the help of torsional weights and a compass needle. A slight decrease in temperature at the junction was quickly compensated. The scientist placed the first end of the thermocouple in a vessel with boiling water, the second - in a container with ice. Uncertainty remained inconsistent temperatures on a scale. For example, boiling begins differently, the process is influenced by the pressure of the atmosphere. But the thermocouple showed itself from the first test much better than a galvanic cell.
Add, torsion balance, whose principle of operation is based on the elastic modulus of a thin wire, designed Pendant. Applied to static charges. Thus, and brought the famous law. The magnetic needle is described in the works of Oersted( 1820).The scientist noticed that the deviation is proportional to what is now called amperage. In that year, Ampère formulated his own famous law, said that a solenoid with a potential difference on its findings is oriented in the Earth’s magnetic field. The discoveries followed one after another, and George Om's book on the mathematical study of the galvanic circuit was the next in a row.
The scientist placed the magnetic needle in the direction of the magnetic meridian. To eliminate the influence of the magnetic field of the Earth. With the help of torsional weights measured the force required to return the system to its original state. Om derived a number of reasons for dissatisfaction with a galvanic cell as a power source:
- Gradually, like any battery, a volt column lost voltage. Om noticed this during the study of the thermal effect on a piece of ordinary wire. Gradually, the temperature inexorably fell. It was necessary to bring the system to the initial state( charge), as the heating increased. Consequently, the galvanic element in the course of the research introduced an error. Thermo-EMF had greater stability and a smaller value, which reduced the heating of the conductors, leveling the temperature error.
- Ohm performed experiments on short lengths of wire cuts from various materials. The resistance of the pieces was less than the internal resistance of the source. As a result of the formation of a resistive divider, the current with a change in the material of the conductor changed extremely little. The internal impedance of the galvanic cell introduced large errors. And here the thermocouple manifested itself in the best way. The internal resistance of such a source is extremely small.
In addition, the purity of the materials of the samples under study was doubtful even by Ohm. There was no digestible tool for estimating the diameter( and sectional area).All this shows how many difficulties the schoolteacher( talented mathematics) had to overcome.
As we got acquainted with the work, it became clear why it took us two whole years to derive a simple formula. To top it off, the scientist did not find support, first of all, material, from academics and state institutions. And the equation was criticized for a long time - the oil in the fire added an inaccuracy in the original formulation of the equation. Summing up:
- By abstraction of a homogeneous, symmetric ring from a conductor, a scientist using a deductive method showed that the current in each section is the same. We believe that Omu actively helped the shooter, whose torsion force on the circumference of the circle remained constant.
- Composing a ring of segments, Ohm created different geometric abstractions, pulled them into a line, drew and introduced the concept of potential difference. And all to see the mathematical expression of the law.
According to Om, the work at that time was considered the most difficult mathematical task, we add, its text will give a hundred points for any modern charade. When a ring is presented as a straight line, it looks strange, the text does not explain this action( although the purpose of the lines is patiently outlined there).We do not undertake to clarify the essence of abstractions, simply indicate the form of the equation to which the scientist arrived:
X = a / b + x,
where X is the force acting on the magnetic needle, a is the length of the conductor under study, b and x are some arbitrary constants. For example, Om proposed to take, respectively, b a single number of 20.25 and x - the range of values from 7285 to 6800. In this case, using the above expression, it was possible to predict in advance the length and material of the conductor magnetic force acting on the arrow. What is considered confirmation of loyalty to what is happening.
Instead of concluding
A talented mathematician worked on a simple addiction two centuries ago for several years. The first helped with this advice, the second interfered. Suffice it to say that the final installation was designed specifically for the purpose of finding dependencies. All parts, including the thermocouple, showed clearly defined dimensions. The installation was covered with a cap to eliminate the effect on torsional scales of air turbulence.
In the end, this reduced the errors to 5–10%.What allowed us to derive the ratio, known today as Ohm's law for the chain segment.