- Introduction
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- Electric current and Current density
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- Drift Velocity
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- Relation between drift velocity and electric current
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- Ohm's Law and Resistance
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- Resistivity and conductivity
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- variation of resistivity with temperature
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- Current Voltage relations
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- Colour code of carbon resistors
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- Combination of Resistors

- Ohm's law is the relation between the potential difference applied to the ends of the conductor and current flowing through the conductor.This law was expressed by George Simon Ohm in 1826

- Statement of Ohm's Law

'if the physical state of the conductor (Temperature and mechanical strain etc) remains unchanged ,then current flowing through a conductor is always ditectly proportional to the potential difference across the two ends of the conductor

Mathematically

V α I

or

V=IR (6)

Where constant of proportionallity R is called the electric resistance or simply resistance of the conductor

- Value of resistance depends upon the nature ,dimension and physically dimensions of the conductor

- Ohm's Law can be deducted using drift velocity relation as given in equation -3 .Thus from the equation

v_{d}=(eE/m)τ

but Now E=V/l

Therfore

v_{d}=(eV/ml)τ

Also I=neAv_{d}

Substituting the value of v_{d}in I relation

I=(ne^{2}Aτ/ml) V (7)

or V/I=(ml/ne^{2}Aτ)=R a constant for a given conductor

Thus

V=IR

Mathematical expression of Ohm's Law

From Ohm's Law

V=IR or R=V/I (8)

Thus electric resitance is the ratio of potential difference across the two ends of conductor and amount of current flowing through the conductor

- electric resistance of a conductor is the obstraction offered by the conductor to the flow of the current through it.

- SI unit of resistance is ohm (Ω) where

1 Ohm=1 volt/1 Ampere

or 1Ω=1VA^{-1 } - Dimension of resistance is [ML
^{2}T^{-3}A^{-2}]

- In terms of drift velocity ,electric current flowing through a conducting wire of length L and uniform area of cross-section A

is

I=dQ/dt =neAv_{d}=(ne^{2}Aτ/ml) V

The above can be rearranged to give the ohm's law i.e,

V=IR

where R=(ml/ne^{2}Aτ) Now R=ρl/A (9)

Where ρ is called the specific resistance or resistivity of the conductor

And ρ=m/ne^{2}τ (10)

- From equation (9) ,we can see that resistance of the wire is proportional to its length and inversly proportional to its cross-sectional area.

- Thus resistance of a long and thin wire will greater then the resistance of short and thick wire of the same material

- Now from equation (9)

R=ρl/A (11)

And from ohm law R=V/I

Therefore

ρ=(V/I)(A/L)

=(V/L) / (I/A)

=E/J (12)

Where E=V/L is the electric field at any point inside the wire and J=I/A is current density at any point in the wire. Unit of resistivity is ohm-meter.

- Thus from equation (12) ,electric resistivity can also be defined as the ratio of electric field intensity at any point in the conductor and the current density at that point.

- The greater the resistivity of the material ,greater would be the field needed to establish a given current densisty

- Perfect conductor have zero resistivities and for perfect insulators resistivity would be infinite
- Metals and alloys have lowest resistivities and insulators have high resistivities and exceeds those of metals by a factor of 10
^{22} - The reciprocal of resistivity is called conductivity and is represented by σ
- Unit of conductivity is ohm
^{-1}meter^{-1}(Ω^{-1}m^{-1}) and

σ is defined as

σ=1/ρ

Since ρ=E/J

or σ=J/E

or J=σE (13a)

- The above relation can also be written in vector form as both J and E are vector quatities where vector
**J**being directed towards**E**

**J**=σ**E**(13b)

Class 12 Maths Class 12 Physics