Ohm's Law | Equation Formula and Limitation of Ohm's Law
The most basic quantities of electricity are voltage, current and resistance or impedance. Ohm's law shows a simple relationship between these three quantities. This law is one of the most basic laws of electricity. This law helps to calculate the power, efficiency, current, voltage and resistance or impedance of any element of electrical circuit.
Ohm's law first appeared in the book written by Georg Simon Ohm (German) in 1827.
The current (I) is directly proportional to the applied voltage (V), provided temperature and all other factors remain constant. Mathematically,
Where, R is constant of proportionality.
This equation presents the statement of Ohm's law. Here, we measure current in Ampere (or amps), voltage in unit of volt.
The constant of proportionality R is the property of the conductor, we know it as resistance and measure it in ohm (Ω). Theoretically, the resistance has no dependence on the applied voltage, or on the flow of current. The value of R changes only if the conditions (like temperature, diameter and length etc.) of the resistor are changed by any means.
History of Ohm's Law
In the month of May 1827, Georg Simon Ohm published a book "Die Galvanische Kette, Mathematisch Bearbeitet". "Die Galvanische Kette, Mathematisch Bearbeitet" means "The Galvanic Circuit Investigated Mathematically". He presented the relationship between voltage (V), current (I), and resistance (R) based on his experimental data, in this book. Georg Simon Ohm had defined the fundamental interrelationship between current, voltage and resistance of a circuit which was later named Ohm's law. Because of this law and his excellence in the field of science and academics, he got the Copley Medal award in 1841. In 1872 the unit of electrical resistance was named 'OHM" in his honor.
Ohm's Law Physics
We can understand the physics behind Ohm's law well if we examine it from atomic level of a metal. A metal conductor contains plenty of free electrons. These free electrons randomly move in the conductor. When, we apply a voltage, across the conductor, the free electrons keep being accelerated towards higher potential end due to electrostatic force of the applied voltage. This means they acquire some kinetic energy as they move towards the + Ve end of the conductor. However, before they get very far they collide with an atom or ion, lose some of their kinetic energy and may bounce back. Again due to presence of static electric field the free electrons again being accelerated. This keeps happening. That means, even after application of external electric field, there will be still random motion in the free electrons of the conductor. Each free electron drifts towards +Ve end with its inherent random motion. As a result, the free electrons tend to "drift" towards the + Ve end, bouncing around from atom to atom on the way. This is how the materials resist a current. If we apply more voltage across the conductor, the more free electrons will move with more acceleration which causes more drift velocity of the electrons. The drift velocity of the electrons is proportional to the applied static electric field. That more electrons pass through a cross section per unit time, which means more charge transfer per unit time. The rate of charge transfer per unit time is current. Hence the current (I) we get is also proportional to the applied voltage (V).
Applications of Ohm's Law
The applications of ohm's law are that it helps us in determining either voltage, current or impedance or resistance of a linear electric circuit when the other two quantities are known to us.
Apart from that, it makes power calculation a lot simpler, like when we know the value of the resistance for a particular circuit element, we need not know both the current and the voltage to calculate the power dissipation since, P = VI.
To replace either the voltage or current in the above expression to produce the result
We can see from the results, that the rate of energy loss varies with the square of the voltage or current. When we double the voltage applied to a circuit, obeying Ohm's law, the rate at which energy is supplied (or power) gets four times bigger. Similarly, the power dissipation at a circuit element is increased by 4 times when we make double the current through it.
Limitation of Ohm's Law
The limitations of Ohm's law are explained as follows:
This law cannot be applied to unilateral networks.
A unilateral network has unilateral elements like diode, transistors, etc., which do not have same voltage current relation for both directions of current.
Ohm's law is also not applicable for non – linear elements.
Non-linear elements are those which do not have current exactly proportional to the applied voltage, that means the resistance value of those elements changes for different values of voltage and current. Examples of non – linear elements are thyristor, electric arc, etc.