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)-