Ohm’s law
Ohm’s law is a fundamental principle in electrical engineering that describes the relationship between electric current, voltage, and resistance.
The law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. Mathematically, Ohm’s law can be expressed as:
I = V / R
where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms.
In other words, if the voltage across a conductor is increased, the current through it will also increase provided the resistance remains constant. Similarly, if the resistance is increased, the current will decrease for a given voltage. Ohm’s law is useful in designing and analyzing electrical circuits, and is one of the fundamental laws in electrical engineering.
Ohm’s law states that the R in this relation is constant and independent of the current. If the resistance is not constant, the previous equation cannot be called Ohm’s law, but it can still be used as a definition of static/DC resistance. Ohm’s law is an empirical relation that accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of the current. However, some materials do not obey Ohm’s law; these are called non-ohmic.
Theory of Ohm’s law
Ohm’s law can be explained at a microscopic level by understanding the behavior of electrons in a conductor.
In a conductor, such as a metal wire, there are free electrons that are able to move through the material. These electrons collide with the atoms of the conductor as they move, which creates a resistance to their motion. The resistance of a conductor is related to the number of collisions that occur as electrons move through it.
When a voltage is applied across a conductor, it creates an electric field that causes the free electrons to move in a particular direction. The electrons experience a force due to this electric field, which causes them to accelerate and move through the conductor. However, the electrons do not move in a straight line but rather undergo a random motion due to collisions with the atoms of the conductor, losing energy and scattering in random directions. This creates resistance to the flow of electrons and causes some of the energy of the electric field to be converted into heat.
Ohm’s law can be understood in terms of this electron behavior. The current through a conductor is directly proportional to the voltage applied across it, because a higher voltage creates a stronger electric field that causes the electrons to move faster, resulting in a higher current. However, the current is inversely proportional to the resistance of the conductor, because a higher resistance means that there are more collisions and, therefore fewer free electrons available to carry the current.
Thus, Ohm’s law can be understood as a balance between the forces driving the electrons (the electric field) and the forces resisting their motion (collisions with atoms), resulting in a relationship between the current, voltage, and resistance of a conductor.
The drift velocity of electrons in a conductor is typically quite slow, on the order of a few millimeters per second, even though the current in the conductor may be quite high. This is because the electrons are constantly colliding with the atoms of the conductor, which slows down their overall motion. Drift velocity is proportional to current. In a resistive material, it is also proportional to the magnitude of an external electric field.
While the drift velocity is relatively slow, it is still an important concept in understanding the behavior of electric currents in conductors. The overall flow of electric charge in a conductor is determined by the combination of the drift velocity and the number of charge carriers moving through the conductor.
For example, when a DC voltage is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity in a 2 mm diameter copper wire in 1 ampere current is approximately 8 cm per hour. AC voltages cause no net movement; the electrons oscillate back and forth in response to the alternating electric field (over a distance of a few micrometers).
