# Formula of drift velocity in terms of potential difference and length of a conductor

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by arka1

2016-02-16T12:34:28+05:30
Drift velocity & Ohm’s lawOHM’S LAW:- Let us consider a conductor through which a current I  is flowing and V be the potential difference between its ends ,then Ohm’s law states that
V ∝ I  or, V = R I ……..(1) where R is the resistance of the conductor. Its SI units of resistance is ohm, and is denoted by Ω.
The resistance R not only depends on the material of the conductor but also on its dimensions .
Resistivity:
-The resistance R of a conductor of length l and cross-sectional area A is found to be ,
R ∝ L and R ∝ 1/A Combining, we have R = ρL /A
where ρ is called resistivity or specific resistance
and ρ depends on the material of the conductor but not on its dimensions.
Current density :-
Using Ohm’s law V = IR = IρL /A
The current density is defined as the current through unit area normal to the current,
I /A = j , is called current density .
The SI units of the current density is A/m2
Ohm’s law in classical form:-
If E is the magnitude of uniform electric field in the conductor whose length is L, then the potential difference V across its ends is EL. Using these, the last equation reads
E L = j ρ L or E = j ρ ……………………(1)
In vector form E = j ρ ……………………(2)
The current density is defined as the current through unit area normal to the current. It is directed along E .
Equation (1)can be written as j = σ E ……………..(2)
where σ = 1/ρ is called the conductivity.
This is Ohm’s law in classical form.