# Ohm’s law and its derivation

**MOBILITY OF THE ELECTRON AND CURRENT**

Mobility of electron (u_{e}) is defined as the drift velocity of electron per unit electric field applied.

u_{e}= drift velocity/electric field= V_{d}/E

Thus V_{d}=u_{e}E

The SI unit of mobility is m^{2}s^{-1}V^{-1} or ms^{-1}N^{-1}C

As by the relation of the current and drift velocity (already discussed)

I=Anev_{d} (1)

By putting value of v_{d} in above equation we get

I=Aneu_{e}E

**OHM’S LAW**

**Statement:**– Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor,provided physical conditions of the conductors such as temperature,mechanical strain etc. Are kept constant i.e. IαV

Or VαI or V= RI

Or V/I=R=a constant

Where R is known as resistance of the conductor . It depends upon the length ,shape and the nature of the material of the conductor. The variation between potential difference (V) and current (I) through a conductor is a straight line.

**Deduction of Ohm’s Law:**

As ** **drift velocity is** **given by V_{d}=eEt/m

But Electric field across the conductor of length l is

E=V/l

Thus V_{d}=e V/ml

Also, I=Anev_{d}

By putting value of v_{d} in the equation of I (equation 1 of relation of the current and drift velocity),we get

I=Ane(eV/ml)=(Ane^{2}/ml)V

Or V/I=ml/Ane^{2}=R

Where R is a constant for a given conductor. It is known as the resistance of the conductor.

Thus V=RI

**This is Ohm’s law.**

** **

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