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Ohm's Law

What is Ohm's Law?

Ohm's Law states that, in an electrical circuit, the current passing through most materials is directly proportional to the potential difference applied across them.

In mathematical terms, this is written as:

V=I/R

where I is the current, V is the potential difference, and R is a proportionality constant called the resistance. The potential difference is also known as the voltage drop, and is sometimes denoted by E or U instead of V.

The SI unit of current is the ampere; that of potential difference is the volt; and that of resistance is the ohm, equal to one volt per ampere. The law is named after the physicist Georg Ohm, who published it in 1826.

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How electrical and other engineers use Ohm's law

Ohm's Law is one of the equations used in the analysis of electrical circuits, whether the analysis is done by engineers or computers. Even though, today, computers running electronic computer aided design and analysis programs do the bulk of the work predicting and optimizing the performance of electrical circuits (in particular, those circuits to be fabricated on silicon chips), most electrical engineers still use Ohm's Law every working day. Whether designing or debugging an electrical circuit, electrical engineers must have a working knowledge of the practical aspects of Ohm's law.

Virtually all electronic circuits have resistive elements which are almost always considered ideal ohmic devices, i.e. they obey Ohm's Law. From the engineer's point of view, resistors (devices that "resist" the flow of electrical current) develop a voltage across their terminal conductors (e.g. the two wires emerging from the device) proportional to the amount of current flowing through the device.

More specifically, the voltage measured across a resistor at a given instant is strictly proportional to the current passing through the resistor at that instant. When a functioning electrical circuit drives a current I, measured in amperes, through a resistor of resistance R, the voltage that develops across the resistor is I R, the value of R serving as the proportionality factor. Thus resistors act like current to voltage converters (just as springs act like displacement to force converters).

Similarly, resistors act like voltage to current converters when a desired voltage is established across the resistor because a current I equal to 1/R times V must be flowing through the resistor. That current must have been supplied by a circuit element functioning as a current source and it must be passed on to a circuit element that serves as a current sink.

The DC resistance of a resistor is always a positive quantity, and the current flowing through a resistor generates (waste) heat in the resistor as it does in one of Ohm's wires. Voltages can be either positive or negative, and are always measured with respect to a reference point. When we say that a point in a circuit has a certain voltage, it is understood that this voltage is really a voltage difference (a two terminal measurement) and that there is an understood, or explicitly stated, reference point, often called ground or common. Currents can be either positive or negative, the sign of the current indicating the direction of current flow. Current flow in a wire consists of the slow drift of electrons due to the influence of a voltage established between two points on the wire.

Since the resistance of a resistor is always positive and the equation describing Ohm's law does not in itself constrain R to be positive (by being written as: |V|=|I| \ R), there is the potential for computing a negative value for R. Using measurements of voltage and current that are made correctly, the sign of a computed R is never negative. When a negative R is computed based on a measurement of the voltage drop across a resistor and a measurement of the current passing through the resistor, then one of the two measurements must have been made improperly. When circuits are analyzed, the direction of flow of current between circuit elements may not be known or obvious. In this case, the direction of the current is assigned arbitrarily. Should a sign error (one that implies a negative resistance) arise during the analysis, the error is resolved by asserting that the initially assigned direction of current was incorrect, and that the actual direction of current is in the direction opposite to the initially assigned direction.

Non-ohmic and active components may actually have negative differential resistance. The word 'differential' is key, though often omitted, because it describes the characteristics of an interesting portion of the I vs. V curve of the non-ohmic device. At no time is the 'static' resistance itself negative.

Certain powered circuit devices, constructed as two terminal devices and tested as if they were a resistor (by applying a voltage across the two terminals while measuring the current), may exhibit actual negative resistance. Ohm's law is not intended to apply to such devices. Further the law of conservation of energy is not violated because there is an integrated source of power.

Ohm's law applies to conductors whose resistance is (substantially) independent of the applied voltage (or equivalently the injected current). That is, Ohm's law only applies to the linear portion of the I vs. V curve centered around the origin. The equation is just too simple to encompass devices described by a more complicated I vs. V relationship.