Ohm’s law proof and limitations of Ohm’s law

Ohm’s law proof and limitations of Ohm’s law

in this topic we will discuss about Ohm’s law proof and limitation of Ohm’s law , in which we will prove Ohm’s law with the help of drift velocity , and graph [V(potential) Vs I(current) ] for non-Ohmic resistance .

Ohm’s law  and deduction of Ohm’s law –

According to Ohm’s law the current flowing through a conductor is directly proportional to the potential difference applied across the conductor when temperature across the conductor is kept constant .

i.e potential difference V α current (I)

or ,  V α I    or,  V = RI   , Where R is the resistance of the conductor which depends on length , shape and nature of the material .

so , we  can write   R=V/I

Deduction of Ohm’s law –

As we know drift velocity Vd = EeƮ/m

But electric field  E = V/l

So  Vd = eV Ʈ/ml ……………(i) ,

We also know that  I = neAVd  therefore Vd = I /neA ……………..(ii)

From equation (i) and (ii)

                                 eV Ʈ/ml = I /neA

so , V = Iml/nA e2 Ʈ

or,  V = I (ml/nA e2 Ʈ) ; here   ml/n Ae2 Ʈ     is constant called resistance

so,  V = RI

or , V α I …………………Hence proved Ohm’s law ,

when we plot the graph potential vs current we get ;

 

Limitation of Ohm’s law ( Non-Ohmic devices ) – As  we know when current flows through some conductor heat developed into the conductor , due to which its property like resistivity changes , and its V/I characteristics also changes . Ohm’s law does not discuss about these kind of change .

Those devices which do not obey the Ohm’s law are called non-Ohmic devices .

V-I characteristics of Non- Ohmic materials –

For junction diode –

 

For  Gallium-Arsenide ( GaAs)-

To know about electrical resistance and resistivity ,and its dependance on the temperature click here-

 

 

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