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
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
but Now E=V/l
Substituting the value of vd in I relation
I=(ne2Aτ/ml) V (7)
V/I=(ml/ne2Aτ)=R a constant for a given conductor
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
Dimension of resistance is [ML2T-3A-2]
(6) Resistivity and conductivity
In terms of drift velocity ,electric current flowing through a conducting wire of length L and uniform area of cross-section A
I=dQ/dt =neAvd=(ne2Aτ/ml) V
The above can be rearranged to give the ohm's law i.e,
Now R=ρl/A (9)
Where ρ is called the specific resistance or resistivity of the conductor
And ρ=m/ne2τ (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)
And from ohm law R=V/I
=(V/L) / (I/A)
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 1022
The reciprocal of resistivity is called conductivity and is represented by σ
Unit of conductivity is ohm-1meter-1(Ω-1m-1) and
σ is defined as
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=σE (13b)
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