Current flows from one charged particle to other when they have some potential difference between them. Basing on this a law called Ohm's law is defined. As per the law the potential difference between the two points is directly proportional to the flow of current between that two points. The proportionality is eliminated with a constant called resistance. It is a physical quantity that measures the opposition to the flow of current. It depends on the nature of the material and its physical dimensions like length and area of cross section of the materiel.
The potential difference is generated between two points using a battery with certain EMF also known as electromotive force. It is not actually force and it is a potential difference between two plates of a cell generated with a certain mechanism which leads to flow of current.
Current is defined as rate of flow of charge. It means it is charge that flows between two points per unit time. It is measured with a unit coulomb per second and is called as ampere. We also know that the charge is quantised. It means it is available as integral multiples of charge of electron. Hence we can find out the number of electrons flow between two points when one ampere current is passing through them as shown in the diagram below.
Resistance can be defined as the potential difference between two points when a current one one ampere is passing between them. Any way resistance does not depends on than rather it is directly proportional to the area of cross section of the conductor and is inversely proportional to the length of the wire.
The materials which has less resistance are capable of passing current through them and they are called conductors. All most all metals comes under this category.
Resistance varies for the same material when it is having different physical dimensions and hence it becomes not usable as a standard way of understanding the opposition to the flow of the current. Thus a proportionality is called as specific resistance or resistivity.
We can define resistivity as the resistance of a wire of unit area of cross section and unit length. It depends on the nature of the material and not on physical dimensions.
Specific resistance can be measured with SI unit called ohm-meter and it is defined as shown below.
Variation of resistance with temperature
Resistance of any material varies with temperature. How does it varies depends on the nature of the material. Some materials resistance increases with temperature and for some other material, it decreases with temperature.
To measure this variation, we need to use a constant called temperature coefficient of resistance. The change in the resistance is directly proportional to its initial resistance and also directly proportional to the rise in temperature. The proportionality is eliminated with a constant and is called coefficient of resistance.
Variation of resistance with length
In general resistance of a wire is inversely proportional to its length when other parameter, area is constant. But if no information is given regarding area in any case, we shall convert that area also in terms of length. We can use the concept that volume of a body remains constant and it is the product of area and length.
Thus it can be proved that resistance is inversely proportional to the square of the length as shown in the written notes below.
Similarly, we can write the variation of resistance only in terms of area,radius and mass of the wire as shown in the below page.
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