- Circuit analysis - Solving current and voltage for every resistor
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Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance ,  one arrives at the usual mathematical equation that describes this relationship: . More specifically, Ohm's law states that the R in this relation is constant, independent of the current.
However some materials do not obey Ohm's law, these are called non-ohmic.
The law was named after the German physicist Georg Ohm , who, in a treatise published in , described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. Ohm explained his experimental results by a slightly more complex equation than the modern form above see History.
In physics, the term Ohm's law is also used to refer to various generalizations of the law; for example the vector form of the law used in electromagnetics and material science:. This reformulation of Ohm's law is due to Gustav Kirchhoff. In January , before Georg Ohm 's work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution. He measured the current by noting how strong a shock he felt as he completed the circuit with his body.
Cavendish wrote that the "velocity" current varied directly as the "degree of electrification" voltage. He did not communicate his results to other scientists at the time,  and his results were unknown until Maxwell published them in He found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions.
Ohm did his work on resistance in the years and , and published his results in as the book Die galvanische Kette, mathematisch bearbeitet "The galvanic circuit investigated mathematically". For experiments, he initially used voltaic piles , but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant voltage. He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature.
He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through the equation. From this, Ohm determined his law of proportionality and published his results. In terms of the length of the wire this becomes,.
Thus, Ohm's coefficients are,. Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity.
We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility. They called his work a "web of naked fancies"  and the German Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science.
These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the s. However, Ohm received recognition for his contributions to science well before he died. In the s, Ohm's law was known as such and was widely considered proved, and alternatives, such as " Barlow's law ", were discredited, in terms of real applications to telegraph system design, as discussed by Samuel F.
Morse in The electron was discovered in by J. Thomson , and it was quickly realized that it is the particle charge carrier that carries electric currents in electric circuits. In the first classical model of electrical conduction, the Drude model , was proposed by Paul Drude , which finally gave a scientific explanation for Ohm's law. In this model, a solid conductor consists of a stationary lattice of atoms ions , with conduction electrons moving randomly in it.
Circuit analysis - Solving current and voltage for every resistor
A voltage across a conductor causes an electric field , which accelerates the electrons in the direction of the electric field, causing a drift of electrons which is the electric current.
However the electrons collide with and scatter off of the atoms, which randomizes their motion, thus converting the kinetic energy added to the electron by the field to heat thermal energy. Using statistical distributions, it can be shown that the average drift velocity of the electrons, and thus the current, is proportional to the electric field, and thus the voltage, over a wide range of voltages.
The development of quantum mechanics in the s modified this picture somewhat, but in modern theories the average drift velocity of electrons can still be shown to be proportional to the electric field, thus deriving Ohm's law. In Arnold Sommerfeld applied the quantum Fermi-Dirac distribution of electron energies to the Drude model, resulting in the free electron model.
A year later, Felix Bloch showed that electrons move in waves Bloch waves through a solid crystal lattice, so scattering off the lattice atoms as postulated in the Drude model is not a major process; the electrons scatter off impurity atoms and defects in the material.
The final successor, the modern quantum band theory of solids, showed that the electrons in a solid cannot take on any energy as assumed in the Drude model but are restricted to energy bands, with gaps between them of energies that electrons are forbidden to have. The size of the band gap is a characteristic of a particular substance which has a great deal to do with its electrical resistivity, explaining why some substances are electrical conductors , some semiconductors , and some insulators.
While the old term for electrical conductance, the mho the inverse of the resistance unit ohm , is still used, a new name, the siemens , was adopted in , honoring Ernst Werner von Siemens. The siemens is preferred in formal papers. In the s, it was discovered that the current through a practical resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson—Nyquist noise , is due to the discrete nature of charge.
Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits. Ohm's law is an empirical law , a generalization from many experiments that have shown that current is approximately proportional to electric field for most materials. It is less fundamental than Maxwell's equations and is not always obeyed.
Any given material will break down under a strong-enough electric field, and some materials of interest in electrical engineering are "non-ohmic" under weak fields. Ohm's law has been observed on a wide range of length scales. In the early 20th century, it was thought that Ohm's law would fail at the atomic scale , but experiments have not borne out this expectation.
As of , researchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide and one atom high. The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; see Classical and quantum conductivity.
Electric Current Exam1 and Problem Solutions
A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in The Drude model treats electrons or other charge carriers like pinballs bouncing among the ions that make up the structure of the material. Electrons will be accelerated in the opposite direction to the electric field by the average electric field at their location.
With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field. The net result is that electrons take a zigzag path due to the collisions, but generally drift in a direction opposing the electric field.
The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions. Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law. A hydraulic analogy is sometimes used to describe Ohm's law.
Water pressure, measured by pascals or PSI , is the analog of voltage because establishing a water pressure difference between two points along a horizontal pipe causes water to flow. Water flow rate, as in liters per second, is the analog of current, as in coulombs per second.
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Finally, flow restrictors—such as apertures placed in pipes between points where the water pressure is measured—are the analog of resistors. We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor. Similarly, the rate of flow of electrical charge, that is, the electric current, through an electrical resistor is proportional to the difference in voltage measured across the resistor.
Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy. In the linear laminar flow region, Poiseuille's law describes the hydraulic resistance of a pipe, but in the turbulent flow region the pressure—flow relations become nonlinear.
Ohm’s Law - How Voltage, Current, and Resistance Relate
The hydraulic analogy to Ohm's law has been used, for example, to approximate blood flow through the circulatory system. In circuit analysis , three equivalent expressions of Ohm's law are used interchangeably:. Each equation is quoted by some sources as the defining relationship of Ohm's law,    or all three are quoted,  or derived from a proportional form,  or even just the two that do not correspond to Ohm's original statement may sometimes be given.
The interchangeability of the equation may be represented by a triangle, where V voltage is placed on the top section, the I current is placed to the left section, and the R resistance is placed to the right. The line that divides the left and right sections indicates multiplication, and the divider between the top and bottom sections indicates division hence the division bar.
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Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R.
In a schematic diagram the resistor is shown as a zig-zag symbol. An element resistor or conductor that behaves according to Ohm's law over some operating range is referred to as an ohmic device or an ohmic resistor because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range. Ohm's law holds for circuits containing only resistive elements no capacitances or inductances for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant DC or time-varying such as AC.
At any instant of time Ohm's law is valid for such circuits. Resistors which are in series or in parallel may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit. When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation , so Ohm's law as defined above does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance "C" or inductance "L".
Equations for time-invariant AC circuits take the same form as Ohm's law. However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials. In any linear time-invariant system , all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.
Current voltage and resistance pdf to word
The complex generalization of resistance is impedance , usually denoted Z ; it can be shown that for an inductor,. This form of Ohm's law, with Z taking the place of R , generalizes the simpler form. When Z is complex, only the real part is responsible for dissipating heat.
In the general AC circuit, Z varies strongly with the frequency parameter s , and so also will the relationship between voltage and current.
The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars. Ohm's law is one of the basic equations used in the analysis of electrical circuits.
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It applies to both metal conductors and circuit components resistors specifically made for this behaviour.
Both are ubiquitous in electrical engineering. If voltage is forced to some value V, then that voltage V divided by measured current I will equal R. Or if the current is forced to some value I, then the measured voltage V divided by that current I is also R.
There are, however, components of electrical circuits which 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 p-n junction diode curve at right. As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current I for a given value of applied voltage V from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage.
Further, the current only increases significantly if the applied voltage is positive, not negative. 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 the dynamic , small-signal , or incremental resistance, defined as the one over the slope of the V—I curve at the average value DC operating point of the voltage that is, one over the derivative of current with respect to voltage.