The basic formulas of Ohm`s law are summarized under Ohm`s triangle. To get a first idea of what is happening, it is possible to compare the electrical situation with that of the water flow in a pipe. The voltage is represented by the water pressure of the pipe, the current is represented by the amount of water flowing through the pipe, and finally the resistance is the equivalent of the size of the pipe. As shown in the following circuit, a supply voltage is 24 V and the current flowing through an unknown resistor is 2 A. Determine the unknown resistance value using Ohm`s law. It was only after considerable effort and in the second attempt that he succeeded in developing what we know today as Ohm`s Law. The development of quantum mechanics in the 1920s changed this picture somewhat, but in modern theories it can still be shown that the average drift velocity of electrons is proportional to the electric field, thus deriving Ohm`s law. In 1927, Arnold Sommerfeld applied the Fermi-Dirac quantum distribution of electronic energies to the Drude model, which led to the free-electron model. A year later, Felix Bloch showed that electrons move by waves (Bloch electrons) through a solid crystal lattice, so that scattering of lattice atoms, as postulated in Drude`s model, is not an important process; Electrons disperse impurity atoms and defects in the material. The latest successor, the modern theory of quantum bands of solids, has shown that electrons in a solid cannot absorb energy, as assumed in Drude`s model, but are limited to bands of energy, with spaces between them of energies that electrons are not allowed to have. The size of the band gap is a characteristic of a particular substance that has a lot to do with its electrical resistance, which is why some substances are electrical conductors, some semiconductors, and some insulators. Thus, using the equation of Ohm`s law, we obtain the voltage drop on the 60 V circuit.

As shown in the following circuit, a supply voltage of 24 V is applied to a resistor of 12 Ω. Determine the current flowing through the resistor using Ohm`s law. If we know two values, we can calculate the third unknown value using Ohm`s law relation. Therefore, Ohm`s law is very useful in electronics and in electrical formulas and calculations. Technicians refer to component nameplates to learn standard voltage and current values. If technicians determine during the test that current readings are not being recorded on their digital multimeters or tweezers, they can use Ohm`s Law to detect which part of a circuit is shaking and determine where a problem might arise. However, there are components of electrical circuits that do not obey Ohm`s law; That is, their relationship between current and voltage (their I-V curve) is nonlinear (or non-ohmic). An example is the transition diode p-n (curve to the right). As can be seen in the figure, the current does not increase linearly with the voltage applied for a diode. A value of current (I) can be determined for a given value of the applied voltage (V) from the curve, but not from Ohm`s law, since the value of the « resistance » as a function of the applied voltage is not constant. In addition, the current increases significantly only if the applied voltage is positive and not negative. The ratio V/I for a point along the nonlinear curve is sometimes called static, cordal or DC resistance,[31][32] but as shown in the figure, the value varies from total V to total I depending on the particular point along the chosen nonlinear curve.

This means that the « DC resistance » V/I at a certain point on the curve is not the same as that which would be determined by applying an AC signal with peak amplitudes ΔV volts or amps ΔI centered at the same point along the curve and measuring ΔV / ΔI. However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of dynamic, small signal or incremental resistance, defined as the slope of the V-I curve at the mean (DC operating point) of the voltage (i.e. above the current dissipation relative to the voltage). For sufficiently small signals, the dynamic resistance makes it possible to calculate the low signal resistance of Ohm`s law as approximately one on the slope of a line drawn tangentially to the V-I curve at the DC operating point. [33] A perfect crystal lattice with a sufficiently weak thermal motion and no deviation from the periodic structure would have no specific strength,[39] but a real metal has crystallographic defects, impurities, multiple isotopes and the thermal motion of atoms. Electrons scatter from all these elements, resulting in resistance to their flow. Mathematically, this current-voltage relationship is written as follows: The formula can be manipulated so that if two quantities are known, the third can be calculated. Drude`s model treats electrons (or other charge carriers) as fins that jump between the ions that make up the structure of the material. The electrons are accelerated in the opposite direction to the electric field by the mean electric field at their location. However, with each collision, the electron is deflected in a random direction, at a speed much greater than the speed gained by the electric field.

The end result is that the electrons zigzag due to collisions, but usually drift in a direction opposite to the electric field. Ohm determined that for normal materials, doubling the voltage doubled the current flow for a particular component. Different materials or the same materials with different shapes have different levels of resistance to current flow. In a true resistive device, the same resistance value of R = V / I is calculated, regardless of the value of the voltage V. That is, the ratio V / I is constant, and if the current is drawn as a function of the voltage, the curve is linear (a straight line). If the voltage is pressed to a value V, then this voltage V divided by the measured current I is equal to R. Or if the current is pressed to a value I, then the measured voltage V divided by this current I is also R. Since the plot of I against V is a straight line, then it is also true that for each set of two different voltages V1 and V2 applied to a given device of resistance R, where the currents I1 = V1 / R and I2 = V2 / R are generated, the ratio (V1 − V2) / (I1 − I2) is also a constant equal to R. The delta operator (Δ) is used to represent a difference in a quantity so that we can write ΔV = V1 − V2 and ΔI = I1 − I2. In summary, for any truly resistive device with resistance R V / I = ΔV / ΔI = R for any voltage or current applied or for the difference between any set of voltages or currents applied.

It can also be said that the resistance to water flow depends on the length of the pipe, the material of the pipe and the height of the tank placed above the ground. The electron was discovered in 1897 by J. J. Thomson was discovered, and it was soon realized that it is the particle (charge carrier) that carries electric currents in electrical circuits. In 1900, the first (classical) model of electrical conduction, the Drude model, was proposed by Paul Drude, who eventually gave a scientific explanation for Ohm`s law. In this model, a solid conductor consists of a stationary lattice of atoms (ions) in which conduction electrons move randomly. A voltage through a conductor causes an electric field that accelerates electrons in the direction of the electric field and causes electron drift, which is the electric current. However, electrons collide with atoms, causing them to disperse and randomize their motion, converting kinetic energy into heat (thermal energy). Using statistical distributions, it can be shown that the average drift velocity of electrons and therefore the current over a wide voltage range is proportional to the electric field and therefore to the voltage.

This formula is called the ohmic loss formula or resistive heating formula. For students of electronics, Ohm`s law (E = IR) is as fundamentally important as Einstein`s equation of relativity (E = mc²) for physicists.

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