__What is known as Specific Resistance?__

*Specific resistance of a material is defined as the electric resistance of that material of unit length and unit cross sectional area.*

- Specific Resistance of a material is also known as
.*Resistivity*

Let, a conductor of length ( l ) and cross sectional area ( A ) has a resistance ( R ) .

Then, the resistance of conductor will depend as –

- R \propto l
- R \propto \left ( \frac { 1 }{ A } \right )

Therefore, \quad R = \rho \left ( \frac { l }{ A } \right ) ………. (1)

Here, ( \rho ) is a *constant of proportionality* which depends upon the material of the conductor. It is known as ** resistivity** or

*of that material.*

**specific resistance**If a conductor is taken such that its length is unit i.e. ( l = 1 ) and area of cross section is also unit i.e. ( A = 1 ) then from equation (1) –

R = \rho \left ( \frac { 1 }{ 1 } \right )

Therefore, \quad \rho = R .

*Hence, resistivity is the resistance of a material body of unit length and unit area i.e. of unit volume.*

### Temperature coefficient of Specific Resistance

Resistivity or specific resistance of a material depends upon temperature of the conductor. It increases with the increase in temperature as shown in figure.

At low temperatures, specific resistance increases at a higher rate as compared with rate of increase at higher temperatures. The relation between specific resistance and temperature is expressed as –

\rho = \rho_0 [ 1 + \alpha ( T - T_0 ) ]

So, \quad ( \rho - \rho_0 ) = [ \rho_0 \alpha ( T - T_0 ) ]

Or, \quad \alpha = \left [ \frac {\left ( \rho - \rho_0 \right )} {\rho_0 \left ( T - T_0 \right )} \right ] …….. (2)

Where ( \rho_0 ) is the resistivity at temperature \left ( T_0 = 0 \degree C \right ) and ( \rho ) is the resistivity at temperature ( T = t \degree C ) and ( \alpha ) is the **temperature coefficient of specific resistance. **

*Therefore, temperature coefficient of specific resistance or resistivity is defined as the rate of change in resistivity by unit temperature change per unit original resistivity.*

Thus, \quad \alpha = \left [ \frac { \left ( \rho - \rho_0 \right )}{ \rho_0 \left ( T - T_0 \right )} \right ]

= \left ( \frac { \Delta \rho }{ \rho_0 \Delta T } \right )

*Temperature coefficient of specific resistance ( \alpha ) is different for different materials.*

__Specific Resistance for Conductors__

For good conducting metals, the resistivity is directly proportional to the temperature.

Therefore, \quad \rho \propto T .

- For good conductors the value of temperature coefficient of resistivity ( \alpha ) is positive.
- Their resistivity increases linearly with increase in temperature as shown in figure (A).
- For most of the metals, resistivity has linear relationship with temperature at normal temperature ranges.

__Specific Resistance for Semiconductors__

For semiconductors, the resistivity decreases with increase in temperature. The variation of resistivity with temperature is given by the relation –

\rho = \rho_0 \ e^{E / 2 k T}

Where ( E ) is energy gap between conduction band and valence band ( k ) is *Boltzmann’s constant* and ( T ) is the *absolute temperature*.

- For semiconductors the value of temperature coefficient of resistivity ( \alpha ) is negative.
- Their resistivity decreases more rapidly with increase in temperature as shown in figure (B).
- At low temperatures, semiconductors behave as
*insulators*but at room temperature they behave as*conductors*.

Examples of semiconductors are Germanium and Silicon etc.

__Specific resistance for Insulators__

- Resistivity of insulators is similar to the resistivity of semiconductors.
- It decreases exponentially with increase in temperature as shown in figure (B).

The variation of resistivity of insulators with temperature is given by the same relation similar to semiconductors –

\rho = \rho_0 \ e^{E / 2 k T} .

- Energy gap ( E ) for insulators is much more than that of semiconductors.

__Electrical Conductance__

*The reciprocal of electric resistance is called **electric conductance.*

Therefore, electric conductance of a conductor is given by –

\quad G = \left ( \frac { 1 }{ R } \right ) .

### Electrical Conductivity

*The reciprocal of electrical resistivity i**s called **electrical conductivity. *

Therefore, electrical conductivity of a material is given by –

\sigma = \left ( \frac { 1 }{ \rho } \right )

- SI unit of conductivity is {\text {ohm}}^{ - 1 } m^{ - 1 } ( \omega^{ - 1 } m^{ -1 } ) or
or**mho per mtr**( Sm**siemen per mtr**^{ -1}).

__Effect of temperature on Electrical Conductivity__

We know that, resistivity of a conductor is directly proportional to the temperature.

Therefore, \quad \rho \propto T .

Also, conductivity is the reciprocal of resistivity. Hence, conductivity is inversely proportional to temperature.

Therefore, \quad \sigma \propto \left ( \frac { 1 }{ T } \right ) .

As the temperature of conductor increases, the conductivity decreases exponentially as shown in figure.

__Super Conductivity__

We know that the *resistance* of conductors increases with increase in *temperature*. Therefore, materials offer low resistance at low temperatures.

*The property of a material which shows almost zero resistance at a very low temperature is called super-conductivity.*

Materials like mercury, lead, alloys and oxides of certain metals etc. shows the property of super-conductivity at very low temperatures. These materials are called **super-conductors.**

Figure shows the behavior of mercury at low temperatures. Resistance of mercury (Hg) drops abruptly to zero below ( 4.2 \ K ) .

*The temperature below which a material becomes super conductor is called **Transition temperature **or **Critical temperature ( T _{c} ).*

- Critical temperature ( T_c ) for mercury is ( 4.2 \ K ) .

__Use of Super Conductors__

*Electrical power* consumption of electrical circuit solely depends upon magnitude of flow of current and *resistance* of circuit. Thus, if an element has zero resistance it means no power loss will occur in that element. Therefore, super-conductors have a number of useful applications because of negligible resistance.

Uses of super-conductors are –

- Coils made of super conducting materials are used for making powerful
*magnets*. - Transmission wires are made of super conducting materials which results for long transmission of electricity without power loss.
- Super conductors are also used in high speed computing machines.
- It is used in thin film devices.