# Electrical resistance and resistivity

In this topic we will discuss about what is Electrical resistance and resistivity (specific resistance). On what factors Electrical resistance and resistivity depends ? And some plot of resistivity with temperature.

Electrical resistance –

It is the property of a conductor to resist the flow of current  through it  or electrical resistance is the obstruction posed by the conductor to the flow of electric current through it . Or Resistance of a conductor is the ratio of potential difference applied across the end of the conductor to the current flowing through it .  i.e R=V/I  ;

the ratio of potential V/s current gives resistance, which is shown in Ohm’s law .

Its unit is Ohm (Ὡ) or Volt /Ampere = V/A

And its dimension is  [ML2T-3A-2]

We can define one ohm as –   resistance of a conductor is said to be 1 Ohm when 1 volt potential difference setup across the end of the conductor and current flows through the conductor is 1 Ampere .

( ********   Cause of the resistance –    As we know even a small piece of the conductor contains millions of free electrons when potential difference setup across the end of the conductors the electric field setup in the conductor due to which electrons start flowing from low to high potential , and the wire arise on account of frequent collision which oppose the flow of charges from one end to other . )

Effect of temperature on resistance –   As we know resistance  R = ml/n Ae2 Ʈ

For a given conductor  R α  1/Ʈ  when the temperature of the conductor is increases then the density remain constant and velocity of the electron increases then relaxation time decreases and hence resistance increases .  So finally we can say  ‘ the value of electrical resistance increases with rise of temperature’ .

The resistance at any temperature  Rt = R0 ( 1 + αt)

Where  Rt – resistance at any temperature ‘T’ , R0 – resistance at temperature 0 kelvin , t is the rise in temperature and α is the coefficient of thermal conductivity .

α = Rt – R0 / R0t

we can define the temperature coefficient of resistance is the increase in resistance per unit original resistance per degree kelvin rise of temperature .  Its unit is per kelvin ( K-1)

for two different temperatures T1 and T2  we can write   α= (R2 – R1 )/ R2(T2-T1 ) ;

[ Question – why alloy like manganin , constantan are used for making standard resistance

Ans- because (i) Alloy have high value of resistivity ,(ii) small value of temperature coefficient (iii) their resistance is less effected by the atmospheric condition .]

Resistivity or specific resistance –

As we know resistance    R = ml/n Ae2 Ʈ  ………….(i)   from this relation we just come to know that resistance is directly proportional to length of the conductor and inversely proportional to area of cross-section the conductor . i.e.  R α l/A

Or , R =ƍl/A………(ii) where ƍ is a constant called resistivity of the conductor ;

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

ƍ = m/n e2 Ʈ  ;

we can define resistivity of a conductor is te resistance of a unit length with unit area of cross-section of the material of the conductor .

Its unit is Ohm-meter (Ὡ-m) and its dimension is   [ ML3T-3A-2] ;

Effect of temperature on resistivity

As we know resistance  ƍ = m/ne2 Ʈ

For a given conductor  ƍ α  1/Ʈ  when the temperature of the conductor is increases then the density remain constant and velocity of the electron increases then relaxation time decreases and hence resistivity increases .  So finally we can say  ‘ the value of electrical resistivity increases with rise of temperature’ .

The resistance at any temperature  ƍ t = ƍ 0 ( 1 + αt)

Where  ƍt – resistivity at any temperature ‘T’ , ƍ 0 – resistance at temperature 0 kelvin , t is the rise in temperature and α is the coefficient of thermal conductivity .

α = ƍ t – ƍ 0 / ƍ0T

we can define the temperature coefficient of resistivity is the increase in resistivity per unit original resistivity per degree kelvin rise of temperature .  Its unit is per kelvin ( K-1)

for two different temperatures T1 and T2

we can write   α = (ƍ2 – ƍ 1 )/ ƍ 2(T2-T1 ) ;

When we plot the graph resistivity or resistance v/s temperature we get the following plot ;

(i) For copper (metal )

(ii) For nickel, iron and chromium  (alloy )

(iii) For chromium

(iv) For semiconductor