Ohm's law
Ohm's law postulates the following relationship: When a voltage is applied to an object, the electric current flowing through changes in its intensity is proportional to the voltage. In other words, the electrical resistance (defined as the quotient of voltage and current) is constant, that is, independent of voltage and current.
In fact, the law applies only on a small scale and only for some substances. Nevertheless, it is the basis for understanding the relationships between current and voltage in electrical circuits.
The name of the law honors Georg Simon Ohm, who could prove this relationship for some simple electrical conductor as the first conclusive.
Description
The proportionality of the voltage to the current is used for defining the magnitude of electrical resistance, of a size that is designated by the symbols. The following applies:
Ohm's Law, but is more than one definition equation: It expresses the proportionality of the current to voltage. Even though, at least to a certain voltage or current range has a system ohmic behavior ( ie, has a constant electrical resistance - called ohmic resistance), so the resistance is often not independent of the current. Even with non- ohmic system behavior can still define a size resistor as a ratio, with a dependence of the resistance eg present. Then, based, inter alia, amplifier circuits. For the description of these processes is often the term is used differential resistance, which detects the correlation between a small change in voltage and the corresponding current change.
Ohm's law can be represented in three formats:
Local approach
In a local viewing Ohm's Law is described by the linear relationship between the current density vector field and the electric field strength vector field with the electrical conductivity as the proportionality factor:
In isotropic materials, the tensor may be replaced by a scalar, and:
The movement of the free electrons considered analogous to the disordered molecular motion in an ideal gas, the constancy of the electrical conductivity appears plausible: The probability density of the electrons is then constant within the conductor. For the mean velocity of the electrons is considered:
The mean distance between collisions of ions in the metal is covered in a typical time:
During this time, the electrons experience an acceleration
By the applied electric field, the elementary charge and the electron mass. The electrons thus achieve with a drift velocity. Substituting this into the equation for a, we obtain:
The sizes and depend only on the velocity distribution within the " electron cloud " from. But since the drift rate is approximately 10 orders of magnitude less than the average speed, the speed distribution is changed by applying an electric field does not, and thus and the whole expression for constant.
History
Georg Simon Ohm was a mathematical relationship - a formula - to develop, with which the " effect of flowing electricity" (now the current) can be calculated depending on the material and the dimensions of a wire. He is not chanced upon the law named after him, but has invested much time and purposeful work. The laws discovered by him in the form seems to us almost as a triviality: The greater the voltage, or the smaller the electrical resistance, the greater the current. These relationships can be very easy to show today with existing in every school test devices with sufficiently low tolerances.
In 1825 ohms were such equipment is not available. Volta columns batteries Daniell elements and so-called trough batteries (which are a plurality of series Daniell elements) in different versions were then as voltage sources. The voltage and current measuring instruments of the time were for Ohms lofty goal rather than detection devices, but not suitable as a sufficient precision instruments, in order to obtain accurate readings for the development of a formula.
Ohms experimental and innovative achievements were to have already developed device components, including the discoveries of several contemporary researchers cleverly combined. He then mathematically analyzed and interpreted their physical context, the measurement data obtained.
First published Ohm 1825 an article in which he described a measuring device developed by him, with which he came to precise measurements in the annals of physics and chemistry than other researchers before him. Ohm used for this purpose on the one hand described in 1820 by Hans Christian Ørsted magnetic effect of electric current on the other hand a very sensitive device for measuring force: he replaced in the measuring device of the Coulomb torsion balance existing in specimens through a small bar magnet, put this torsion balance on a current-carrying wire and measure the force effect of the current to the magnet. This measurement he performed with various wires and then looked for a mathematical relationship between wires and forces.
However, the 1825 Preliminary in Article indicator of the law, according to which metals the Contactelectricität guide published measurement results could not lead to a universal formula because - analyzed by today's standards - the electrical power of all then use voltage sources ( among others, by varying the formation of gas bubbles on the metal plates ) varies greatly. This effect is described by Ohm several times: the " effect on the needle " change during the individual measurements and is dependent, among other things, on the order of the measurements made. Nevertheless, he managed in the published articles from his readings ultimately from a formula that reproduces the measured values given as approximate.
As a result of his article Ohm received a notice to the discovery of the thermocouple by Thomas Johann Seebeck, about 1823, drawn up by Ørsted report in the Annals was published. This note helped ohms to his breakthrough.
In determining the law according to which metals conduct Contactelektricität described Ohm 1826 first critical look at the " constant waves of force " in his previous attempts. Following is the description of a designed by him " torsion balance ", which he had make of a craftsman ( see figure). The bow- shaped member abb'a ' is a thermal element made of a bismuth arms on the legs of each of a strip of copper is fastened. One leg was heated with boiling water, and the other cooled with ice water. Ohm continued his experiments in January 1826. The vessels for the temperature baths are not shown. The reproducible temperature difference of about 100 ° C between the legs of the bracket generates a reproducible " exciting force ", the uncontrolled " surging " because here no chemical reactions. According to today's definitions corresponds to this " exciting force " an open circuit voltage of about 7.9 mV.
Ohms measured the forces acting on the magnetic needle, when he dipped the ends of different length wires into the mercury -filled " egg cup " and. From the measurement data obtained in this he developed the formula. Here is the electric current for the " exciting force ", stands for the line resistance of the torsion balance (including power source) and for the length of the resistance wires used. In another article of the same year ohms used the term " voltage " instead of " exciting force ".
Thus, the formula is exactly the same equation that we use today in a circuit for the description of the relationships: (: internal resistance of the power source; outdoor resistance of the connected to the power source components). With the help of the thermocouple it ohms was so successful that to discover the law named after him.
Published in 1827 Ohm The galvanic chain processed mathematically, where he again took up not only the dependence of the current on the material of the wire. Among other things, he led forth the theory, supported by its measurements as a function of the current from the conductor length and the cable cross -section. The relationships for series and parallel connection of resistors have been described by conclusive.
In his publications of 1826/27 Ohm explained - then "just" a teacher of physics and mathematics - the observations of many renowned scientist different from what they had done. This may be the reason that the importance of his work was not accepted by the scientific community immediately: " Only in the course of the 30 years of his law was reluctantly accepted in Germany; internationally it was taken only after a Nachentdeckung in 1837 to the attention. "