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State ohms law and deduce it from drift velocity concept

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State and derive Ohm's law using concept of drift velocity

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➡ Statement of Ohm's Law :

⭐Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference across its two ends, provided that the physical conditions ( temperature, mechanical strain, etc ) remain constant. ...

⭐ Electric current is defined as the rate of flow of electric chargethrough a conductor.

➡Derivation :

➡Consider a current of length l and cross sectional area A. When a potential difference V is applied across its ends, the current produced is I. If n is the number of electrons per unit volume in the conductor and vd the drift velocity of electrons, then the relation between current and drift velocity is

I=neAvd .........(i)

Where e is the electric charge on the electron.

Electric field produced at each point of wire, E=Vl ............(ii)

If τ is the relaxation time and E is the electric field strength, then drift velocity

vd=eτEm .............(iii)

Substituting this value in equation (i), we get

I=neA(eτEm)or, I=ne2τmAE ...........(iv)

From equation (ii)

I=ne2τAmVlor, VI=mne2τlA ...............(v)

Under given physical conditions such as temperature, pressure etc., for a given conductor

mne2τlA=R=a constant .........(vi)

For a given conductor, R is a constant and is known as the resistance of the conductor.

Thus, from equation (v) and (vi)

VI=R

This Ohm's law.

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