Ohms Law

Ohms Law Statement - Limitations and Applications of Ohms Law

Ohm’s law is one of the most important law in the study of physics and electrical components and their properties. George Ohm published his work on-resistances in the year 1827. Gathering inspiration from the previous scientists who worked on resistance and the related theories, Ohm formulated Ohm's law. The law is basically a description of electricity and how it works, quantitively. To focus on his experiment:

Ohm used a thermocouple which is a stable source of voltage when it comes to internal resistance and a constant source of voltage. In order to measure the voltage, he used a galvanometer. Ohm was aware of the fact that the temperature of the junction is proportional to the voltage across the two terminals of the thermocouple. To complete the circuit, or to make it a closed circuit, he used various wires of varying length, properties, and diameter. The results that he got could be arrived at upon the basis of the equation:

X=a/(b+l), Where x is the reading of the galvanometer, a is a constant dependent upon the junction temperature of the junction, b is a constant and l is the length of the conductor used.

In light of the above equation, he derived the law of proportionality as
I=E/(r+Rl), Where E is the thermocouple emf, internal resistance is r and R is the test wire resistance per unit length.
Impressed by his work, which leads to many more discoveries, the works of Ohm was referred to as a "web of naked fancies".
According to Ohm's law, the value of the current flowing through a conductor is directly proportional to the value of the potential difference applied across two terminals. The equation of Ohm's law is I= V/R, here the constant of proportionality is R that is the resistance, V is the voltage and I is the current flowing through the wire. In this law, the resistance is considered to be constant and is not dependent on the current flowing through it. The unit of R is ohm, I is Ampere and V is volts, in the standard units. The law also defines the conductivity of a material through which current is flowing.
Ohm’s law is often generalized in physics for many other applications.

The empirical law that is Ohm's law, in its generalized form, states that current is proportional to the electric field. But this generalization is not applicable for all the materials. Some materials can break down in the presence of a very strong electric field and some materials do not obey this law in the presence of weak electric fields. Such materials which do not obey Ohm's law are known as non-ohmic materials. But when this law is obeyed, it is applicable even at very minute scales such as atomic scale.

In electromagnetics, it is used in its vector form which states that J= σE. Here j is considered as the current density at a particular location of the material, E is the electric field and σ is known as conductivity which is a property of the material used.
In order to understand Ohm's law, we need to understand three basic principles, that being, voltage, current and resistance.
Voltage: The amount of energy given per Coulomb is known as voltage. It can also be described as the amount of potential energy between the two terminals. 1V is defined as the potential difference between two terminals which will give us 1 Joule of energy per Coulomb of charges that is passing through it.

Resistance: The property of a material due to the virtue of which it tends to resist the flow of current through it is known as resistance. Thus, the circuit in which the value of resistance is more will allow a smaller number of charges to flow through it and the one which has less value of resistance will allow a number of electrons to flow and thus support of the amount of current flowing through it.

In a wire which has a uniform cross-sectional area, the value of resistance will depend upon the value of an area of cross-section and the length of the wire. It is directly proportional to l/A.

R = ρ

Resistance also depends upon the temperature of the conductor.

Current: The rate of flow of charges through a particular cross-sectional area is known as current. In other words, 1 A is described as the amount of current when 1C of charge or 6.24 x 10-19 electrons are passing through a cross-sectional area per unit of time.

Some other important parameters are as follows:

Drift speed: In a conductor, the ions present are mobile and move in a haphazard manner constantly. For the existence of net charge flow, it is necessary that the particles move along together with average velocity. In metallic particles, electrons are the charge carriers which move in the direction opposite to that of the electric current flowing through the conductor. The movement is in a random direction. This speed or drift is known as the drift speed. The value of the drift speed can be calculated by the equation:

I=nAvQ, where n is the number of the charge carriers per unit volume, A is the area of a cross-section through which current is flowing, v is the average drift speed, I is the current and Q is the value of charge on each carrier. Usually, the speed or the drift speed of electrons in a conductor is very less. For example, let's take a copper wire whose area of cross-section is 0.5 mm2 and the current flowing through it is 5 A. So, the drift velocity of the particles will be in the millimeter order that too per second.
Resistivity: The reciprocal of conductivity is known as resistivity.
E=ρJ where ρ is known as resistivity.

LIMITATIONS OF OHM’S LAW:

Ohm’s law is not devoid of limitations. Those are:
In unilateral networks or the networks which allow the flow of current only in one direction and comprises of other electrical elements such as a diode, transistor etc, the Ohm's law fails and cannot be applied in the network.

The non-linear elements, or the elements in which the current is not definitely proportional to the voltage applied. In such elements, the resistance is not a constant value and keeps changing with the change in the value of applied voltage and current. Hence such elements do not obey the Ohm's law which changes the value of resistance.

APPLICATIONS OF OHM’S LAW:

Ohm's law helps us in determining the values of resistance, the current flowing through a circuit, the voltage applied. Hence with the help of these values, we can find the values of other factors like drift speed, resistivity and many more. It also allows us to calculate the value of power consumption.

USES IN DAILY LIFE:

Being a fundamental law, Ohm's law has many practical applications in electrical components and hence electrical appliances. Let's focus on some of the practical usages of Ohm's law we come across in our day to day lives.

Used to control the speed of fans: We all know what a potentiometer is. The electrical component whose resistance has got a variable value is known as a potentiometer. To control the speed of a standard fan, a potentiometer could be used. This is achieved by using a circular knob. The knob is fixed on the component. This knob is rotated and is used to achieve the desired value of the resistance on the output component. Hence, for a particular resistance value of the input, we can calculate the value of resistance, the current flowing. So, it provides us with the knowledge of power. These values are calculated with the help of Ohm’s law.

Required wattage sizing of components: In order to operate any electrical appliances such as iron, an electric kettle and many more, a huge number of resistors are used. They are required for the proper functioning of these appliances. To achieve the proper operation, proper wattage sizing of these resistors is required. Power is calculated by the formula, P=VI.

Power consumed, and the power supplied by an electronic device: The coil used in the heater and the voltage which is applied helps us to find the power of the electrical heater. When this is calculated, power is multiplied by the duration of time for which it was used and also the number of days then we get the amount we need to pay according to the electricity bill.

Fuses: Ohm's law is also useful in deciding the fuses to be used. In order to protect a circuit, fuses and circuit breakers are used. These are connected in series with the electrical appliances. Ohm's law allows us to find the value of the current which could flow through the fuses. If the current value is too large, then it could damage the circuit and even lead to the explosion of the electronic device. There are two cases where Ohm's law could be used in order to select fuses. First is when the resistance is known and the other is when the resistance value is not known.