Ohm’s Law

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Ohm’s law, a fundamental law describing the relationship between Current, Voltage, and Resistance, was discovered by the German Physicist, Georg Simon Ohm, and was first published in 1827. This formulation forms the basis of our understanding about DC electrical circuits, and the science of electrical currents in general. Formally, Ohm’s Law states that the current running through a conductor is directly proportional to voltage. Or more specifically:

The potential difference across a conductor is proportional to the current through it.

Current describes the flow of electrical charge through a conductor and is considered a flow. Voltage is a force which affects this flow of current, or energy through a conductor between two particular points. Voltage is thus a measure of potential energy present to move charge between two points in a circuit.

The third factor in Ohm’s Law which Ohm published, in his paper The Galvanic Circuit Investigated Mathematically, is the phenomenon of resistance. He found that the movement of the current through a conductor is subject to friction, or resistance. Resistance and Voltage are thus similar and work in opposite directions as they impact the flow of current traveling between 2 points. Resistance is also termed the constant of proportionality

Thus, the complete law states that Current is directly proportional to Voltage, and inversely proportional to Resistance.

Considering the formal phrasing where Voltage, or the potential difference across a circuit, is proportional to the current, with resistance as the constant defining this proportion, Ohm’s Law is given by the following formula:

 V = IR


V = voltage and is measured in volts (V);

I = current and is measured in amperes (A) and

R = resistance which is measured in Ohms


What Ohms law defines is the phenomenon where R is constant. This is an empirical relation and has proven reliable in the case of most conductive materials. When R is a constant, we say that that the material is ‘ohmic’ in that it obeys Ohm’s Law, because the potential difference (or voltage) varies linearly.

The formula is more commonly presented as follows:


I = V / R


Electrical Power in Circuits

Prior to Ohms work, others ventured to understand the occurrence of electrical power, and how this varied in different materials, across different lengths and so on. Electrical power is essentially the rate at which energy can be absorbed or produced. Voltage is the source of energy, which, when applied, produces power to the circuit, which flows as a current. The higher the value of this voltage, the more electrical power is going to be. This means a brighter light or a hotter heater. Power is measured in Watts and is the product of the voltage and the current.

This is shown as follows:

P = V x I


Combining this with Ohm’s Law, we find the following also hold:


P = V / R



P = I x R


You could also use the free Ohm’s Law calculatorLinks to an external site..

From these formulations, we can remember these formulae represented in the following triangles. This is an easy way to remember these critical relationships in calculating electrical circuits.


Ohm’s Law Triangle

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Power Triangle

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These two formulations together allow us to determine the energy required (input), as well as the power output of electrical circuits. Or use the free Ohm’s Law calculator for even quicker results!


The Coulomb

The Coulomb is a measure of electrical charge which is proportional to the number of electrons in an imbalanced state. This measure is rarely used, but is interesting, as one ampere is equal to 1 coulomb of charge which passes by a given point in a second. 1 coulomb of charge is equal to the charge carried by 6.424 x 1018 electrons.  From this, one can understand current as the rate of electric charge in the motion of electrons through a conductor.


Advanced applications of Ohm’s Law



The vector form of Ohm’s Law is used in electromagnetics in the following form:


J = σE



J = the density of the current at a given location in the material;

E = a measure of the electrical field, and

σ = a measure of conductivity.

This formulation was developed by Gustav Kirchhoff, who developed a series of circuit laws used extensively in electrical engineering. These were developed in his years as a student in 1845.


Biological Applications

In biology, conductance is used where;

g = 1 / R


In this case, Ohm’s Law is thus stated as follows:


I = gV


In this case, electrical conductance is the inverse of electrical resistance. Conductance is a measure of the ease with which current can flow between two points in a circuit. This is measured in Siemens (S). Just like resistance, conductance depends on what the material is made of. Rubber does not conduct electricity, while metals would have a higher conductance.


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