OHM'S LAW

We have seen that when a battery is connected across a conductor, an electric current begins. 

How much current flows through the conductor when a certain potential difference is set up across its ends? 

The answer to this question was given by a German Physicist George Simon Ohm. 

He showed by elaborate experiments that the current through a metallic conductor is directly proportional to the potential difference across its ends. This fact is known as Ohms' law which states that

"The current flowing through a conductor is directly proportional to the potential difference across its ends provided the physical state such as temperature etc of the conductor remains constant."

Symbolically Ohm's law can be written as

Ι ∝ ν

It implies that

V=RI

where R, the constant of proportionality is called the resistance of the conductor. 

The value of the resistance depends upon the nature, dimensions and the physical state of the conductor.  

Define resistance.

The resistance is a measure of the opposition to the motion of electrons due to their continuous bumping with the atoms of the lattice. 

Unit of resistance.

The unit of resistance is ohm. 

One ohm.

A conductor has a resistance of 1 ohm if a current of 1 ampere flows through it when a potential difference of 1 volt is applied across its ends. 

The symbol of ohm is Ω. 

If I is measured in amperes, V in volts, then R is measured in ohms i.e.

R(ohms)=V (volts)/I (amperes)

Ohmic Conductors

A sample of a conductor is said to obey Ohm's law if its resistance R remains constant that is, the graph of its V versus I is exactly a straight line. A conductor which strictly obeys Ohm's law is called ohmic. 

Non Ohmic Conductors

There are devices, which do not obey Ohms' law i.e., they are non ohmic. The examples of non ohmic devices are filament bulbs and semiconductor diodes.

Let us apply a certain potential difference across the terminals of a filament lamp and measure the resulting current passing through it. If we repeat the measurement for different values of potential difference and draw a graph of voltage V versus current 7, it will be seen that the graph is not a straight line. It means that a filament is a non ohmic device. This deviation of I-V graph from straight line is due to the increase in the resistance of the filament with temperature.

As the current passing through the filament is increased from zero, the graph is a straight line in the initial stage because the change in the resistance of the filament with temperature due to small current is not appreciable. As the current is further increased, the resistance of the filament continues to increase due to rise in its temperature.

Another example of non ohmic device is a semiconductor diode. The current - voltage plot of such a diode is shown in Figure. The graph is not a straight line so semi conductor is also a non ohmic device.

Review of Series and Parallel Combinations of Resistors

In an electrical circuit, usually, a number of resistors are connected together. There are two arrangements in which resistors can be connected with each other., one is known as series arrangement and other one as parallel arrangement.

Series Combination of resistance 

If the resistors are connected end to end such that the same current passes through all of them, they are said to be connected in series as shown in Figure. There equivalent resistance R, is given by

R_eq=R₁+R₂+R₃+------

Parallel combination of resistance 

In parallel arrangement a number of resistors are. connected side by side with their ends joined together at two common points as shown. in Figure. The equivalent resistance R. of this arrangement is given by 

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃+..........