Definition of Resistance

 

Electrical resistance may be defined as the basic property of any substance due to which it opposes the flow of current through it. While a voltage is applied across any substance, current starts flowing through it. But if we observe carefully, the current flows through the all substances are not equal even when the same voltage is applied across each of the substances. This is because current carrying capacity of all substances is not equal. The current depends upon the number of electrons' crosses the cross-section per unit time. Again this number of electrons crossing the cross-section is dependable on the free electrons available in the substances. If free electrons are plenty in a substance, the amount of current is more for same applied voltage across the substances. The current through a substance not only depends upon the number of free electrons in it, but also depends upon the length of path an electron has to travel to reach from lower potential end to higher potential end of the substance. In addition to that, every electron has to collide randomly with other atoms and electrons in numbers of times during its traveling. So, every substance has a property to resist current through it and this property is known as electric resistance.

 

If one volt across a conductor produces one ampere of current through it, then the resistance of the conductor is said to be one ohm (Ω).

 

Laws of Resistance

There are mainly two laws of resistance from which the resistivity or specific resistance of any substance can easily be determined. One law is related to cross-sectional area of the conductor and other law is related with its length.

 

 

As stated earlier, the current through any conductor depends upon number of electrons passes through a cross-section per unit time. So if cross section of any conductor is large then more electrons can cross it that means more current can flow through the conductor. For fixed voltage, more current means less electrical resistance. So it can be concluded like that resistance of any conductor is inversely proportional to its cross-sectional area.

 

If the length of the conductor is increased, the path traveled by the electrons is also increased. If electrons travel long, they collide more and consequently the number of electron passing through the conductor becomes less; hence current through the conductor is reduced. In other word, resistance of the conductor increases with increase in length of the conductor.

 

The laws of resistance state that, Electrical resistance R of a conductor or wire is

 

• directly proportional to its length, l i.e. R ∝ l,

• inversely proportional to its area of cross-section, a i.e.

 

 

ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or wire. Now if we put, l = 1 and a = 1 in the equation,

 

We get, R = ρ. That means resistance of a material of unit length having unit cross - sectional area is equal to its resistivity or specific resistance. Resistivity of a material can be alliteratively defined as the electrical resistance between opposite faces of a unit cube of that material. Hence we have seen that laws of resistance are very simple.

 

 

Resistance Variation with Temperature

There are some materials mainly metals, such as silver, copper, aluminum, which have plenty of free electrons. Hence this type of materials can conduct current easily that means they are least resistive. But the resistivity of these materials is highly dependable upon their temperature. Generally metals offer more electrical resistance if temperature is increased. On the other hand the resistance offered by a non - metallic substance normally decreases with increase of temperature. If we take a piece of pure metal and make its temperature 0° by means of ice and then increase its temperature from gradually from 0°C to to 100°C by heating it. During increasing of temperature if we take its resistance at a regular interval, we will find that electrical resistance of the metal piece is gradually increased with increase in temperature. If we plot the resistance variation with temperature i.e. resistance Vs temperature graph, we will get a straight line as shown in the figure below. If this straight line is extended behind the resistance axis, it will cut the temperature axis at some temperature, − t0°C. From the graph it is clear that, at this temperature the electrical resistance of the metal becomes zero. This temperature is referred as inferred zero resistance temperature. Although zero resistance of any substance cannot be possible practically. Actually rate of resistance variation with temperature is not constant throughout all range of temperature. The change in electrical resistance of any substance due to temperature rise mainly depends upon three factors-

 

• The value of resistance at initial temperature,

• Rise of temperature and

• the αo.

 

This αo is different for different materials, so effect on resistance at different temperature are different in different materials.

 

So the temperature coefficient of resistance at 0°C of any substance is the reciprocal of the inferred zero resistance temperature of that substance.