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page 4 XII PHYSICS UNIT 2


page 4

relation between current & drift velocity

consider a conductor of length(l)  &  cross sectional area (a)  

volume of the conductor =A×l
 if n be the number of free electron per unit volume
then total number of free electrons=n×A×l
total charge in the conductor q= n×A×l×e (due to all free electron) 

now time taken by electron to cross the length (l) of the conductor 

  t=l/vd      where vd is drift velocity of the electrons
I =q/t or I = (n×e×A×l×vd) /l or I =n×e×A×vd
since n, A, e are constant.
so I { vd 

hence current flowing in a conductor is directly proportional to the drift velocity. 

Deduction of ohm's law

the drift velocity is given by
    vd =(e×E×T) /m  =(e×v×T) /ml
also I= n×e×A×vd  =( n×e×A×e×v×T) /ml
or v/l= (m×l) /n×e^2×T×A

at fixed temp. m, l, n, e, T & A are all constant for a given conductor 

therefore v/l =constant=R, this is ohm's law

where R=(m×l) /(n×e^2×T×A)  is constant for a given conductor 

it is know as resistance of conductor. 

it is clear that resistance of the conductor depends upon:
1.shape &size of the conductor
2.nature of the material of the conductor.
3.physical condition of the conductor. 

Resistivity in terms of electron density & relaxation time

we know R= (p×l) /A
      and R= (m×l) / (n×e^2×T×A)
compare these two eq.
we get p= m/(n×e^2×T) 

that means p (resistivity)  depends n & T 
further we can say that p depends on nature of the material & physical condition.  it doesn't depends upon the shape & size of the conductor

current density (J) 

current per unit cross sectional area is called current density .

    J= I/A   or J= (n×e×A×vd) /A or J= n×e×vd 

it is vector quantity 

S. I unit Am^-2
dimension formula [L^-2A]

relation between current density (J), conductivity & electric field (E) 

current density(J)  = n×e×vd or J= (n×e×e×E×T) /m  = (n× e^2 ×T× E) /m 

or J= (1/p) ×E          where m/(n×e^2×T) =p

 or J= sigma×E   where sigma = 1/p




      


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Location: Panipat, Haryana, India

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