# Electric Resistance | Resistivity | Definition | Formula

When the voltage is applied to an electrical circuit, the free electrons starts moving. When they are moving they collide with the other atoms and molecules of the substance. These collisions offer opposition to the flow of electrons or current called electric resistance.

# Electric Resistance Definition | Formula | Explanation

Hence, the opposition offered to the flow of current is called electric resistance. The resistance is represented by R. Unit of electric resistance is ohm and it is denoted by symbol Ω.

The resistance of a conductor depends on the following factors:

• It is directly proportional to the length of the conductor, i.e. R α l
• The resistance of the conductor is inversely proportional to its area of cross-section, i.e. R α 1/a

Therefore, R α l/a

or     R = ρl/a

Where ρ is a constant called resistivity of material by which conductor is made of. It depends upon the nature of the material used in conductor manufacturing. The electric resistance of the conductor also depends upon the temperature of the wire. But it will be discussed later.

The electrical resistance of metals is small in comparison to certain materials like wood, glass, plastic etc. Thus, metals are known as good conductors of electric current.

Whereas materials like wood, glass, plastic etc., do not allow the current to pass through them easily and are known as bad conductors or insulators.

# Resistivity | Specific Resistance Definition | Explanation | Formula

As we know that, resistance, R = ρl/a

If l = 1m, a = 1m2, then R = ρ

Hence, resistivity or specific resistance of a material may be defined as the resistance offered by the one-meter length of material having an area of the cross-section of one square meter.

We know that, Resistance, R = ρl/a

Or  ρ = Ra/l

Putting the units of various quantities as per SI units, we get,

ρ =  (ohm x m2)/m = ohm-m

Hence, the unit of resistivity or specific resistance is ohm-meter in SI units. A smaller unit of resistivity is ohm-cm.

## Combination of Resistances

In many practical applications, two or more resistances are required to be combined. This can be done in two ways: (i) In Series and (ii) In parallel. Sometimes resistances are to be combined in such a way that some resistances are in series and some in parallel. Such a combination is called the mixed grouping.

If in an electrical circuit two or more resistances connected between two points are replaced by a single resistance such that there is no change in the current of the circuit and the potential difference between those two points, then the single resistance is called the ‘equivalent resistance’.
The equivalent resistance connected in series and in parallel is calculated in the following way:

## Combination of Resistances in Series

In this combination, the resistances are connected end to end. Thus the second end of each resistance is joined to the first end of the next resistance and so on.

In this combination, the same current flows in all the resistances but the potential differences between their ends are different according to their resistances.

In Figure, three resistors AB, BC and CD are connected in series. Suppose their resistances are R1, R2 and R3 respectively. Let the equivalent resistance of these resistances be R.

Suppose a current I is flowing in all the three resistances and the potential difference between the ends of the resistances R1, R2 and R3 are V1, V2 and V3 respectively.

Then, according to the definition of resistance, we have
V1 = I R1, V2 = I R2 and V3 = I R3.

If the potential difference between A and D be V, then

V = V1 + V2 + V3 = I R1 + I R2 + I R3

V = I (R1 + R2 + R3) …….(i)

The equivalent resistance between A and D is R. Therefore,

V = I R ……….(i)

Comparing equation (i) and (ii), we get

I R = I R1 + I R2 + IR2

or   R = R1 + R2 + R3

Thus, the equivalent resistance of the resistance connected in series is equal to the sum of those resistances. It is evident that in series the value of the equivalent resistance is greater than the individual value of each resistance.

## Combination of Resistances in Parallel

When two or more resistances are combined in such a way that their first ends are connected to one point and the second ends are connected to another point then this combination is in parallel.

In this combination, the potential difference between the ends of all the resistances is the same but the current in different resistances are different.

In Figure, three resistances R1, R2 and R3 are joined in parallel between points A and B. Suppose the current flowing from the cell is I.

At the point A, the current is divided into three parts. Suppose I1, I2 and I3 are the currents in R1, R2 and R3 respectively. At point B, these currents meet and form the main current I.

Thus, we have
I = I1 + I2 + I3 ……..(i)

Let the potential difference between the points A and B be V. Since each resistance is connected between A and B, the potential difference between the ends of each will be V. Therefore,

I1 = V/R1I2 = V/R2I3 = V/R3

Substituting these values in equation (i), we get

I = V/R1 + V/R2 + V/R3 ………..(ii)

If the equivalent resistance between the points A and B be R, then
I = V/R …….(iii)

Comparing equation (ii) and (ii), we get

V/R = V/R1 + V/R2 + V/R3

or   1/R = 1/R1 + 1/R2 + 1/R3

That is, the reciprocal of the equivalent resistance of the resistances connected in parallel is equal to the sum of the reciprocals of those resistances.

The value of the equivalent resistance of the resistances connected in parallel is less than the value of the smallest resistance among those resistances.

In our house the various electric appliances like bulbs, fans, heater etc. are connected in parallel to one another and all have their separate switches. Thus each of them has a definite potential difference across it and the current flowing in it does not depend upon whether any other bulb or fan is ON or OFF.

As we close the switches of the other bulbs and fans, the total resistance of the house goes on decreasing and the current drawn from the mains goes on increasing.

## Effect of Temperature on Resistance

Generally, the resistance of every material changes with the change in temperature. The effect of temperature upon resistance varies according to the type of material as discussed below:

Pure Metals: The resistance of pure metals like copper, aluminum silver etc. increases with the increase in temperature. This increase in resistance is large and uniform for normal ranges of temperature.

Alloys: The resistance of alloys increases with increase in temperature but the increase in resistance is very small and irregular. In the case of the alloys like Eureka, Manganin, Constantan etc., the increase in resistance is almost negligible over a considerable range of temperature.

Semiconductors, Insulators and Electrolytes: The resistance of semiconductors, insulators and electrolytes decreases with the increase in temperature.

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