Ohm’s Law
On the basis of his experimental observations, a German physicist George Simon Ohm derived a relationship between electric current and potential difference. This relationship is called as Ohm’s law.
Ohm’s law can be stated as
The current flowing through a conductor is directly proportional to the potential difference applied across its ends provided the physical conditions like temperature, pressure, humidity, strain etc remains unchanged. 
Mathematically,
Potential difference ∝ Current
V ∝ I
or
where R is a constant of proportionality called as resistance of conductor.
Ohm’s Law Graphs
The following graphs are plotted between the potential difference V applied across the conductor to the current flowing through it.
VI Graph:
On comparing V = RI with y = mx, we conclude that
 The graph between V (plotted on Yaxis) and I (plotted on Xaxis) is a straight line passing through origin.
 The slope of VI graph = resistance of conductor.
IV Graph:
The equation V = RI can be written as I = (1/R)V.
On comparing I = (1/R)V with y = mx, we conclude that
 The graph between I (plotted on Yaxis) and V (plotted on Xaxis) is a straight line passing through origin.
 The slope of IV graph = 1/R = G = conductance of conductor.
Vector Form of Ohm’s Law
If E is the magnitude of electric field in a conductor of length L, then the potential difference across its ends is
(Equation01)
Also, we know the resistance of a conductor having length L & area of crosssection A is given by
(Equation02)
Substituting Equations01 and 02 in the scalar form of Ohm’s law V = IR, we get
As the direction of current density j is same as that of electric field E, we can write the above equation in vector form as
Since ρ = 1 / σ, so the above equation can also be written as
The above two equations represent the Ohm’s law in vector form.
Ohmic Vs NonOhmic Conductors
Ohm’s law is obeyed by many substances under certain conditions but it is not a fundamental law of nature.
Ohmic Conductors 
NonOhmic Conductors 
Ohmic conductors are those which obey Ohm’s law.  Nonohmic conductors are those which do not obey Ohm’s law. 
The resistance of ohmic conductors is constant at a given temperature.  The resistance of nonohmic conductors is not constant even at a given temperature. 
The resistance is independent of the current through the conductor.  The resistance of such conductors is current dependent. 
For ohmic conductors, the linear relationship between voltage and current holds good.  For nonohmic conductors, situations may be of types

Examples of ohmic conductors copper, silver etc.  Examples of nonohmic conductors pn junction diode, thyristor, GaAs etc. 
Limitations of Ohm’s Law
Ohm’s law is not a fundamental law of nature.
 It is not applicable to unilateral networks which allow the current to flow in one direction. Such types of network consist of elements like diode, transistor etc.
 It is not applicable to nonlinear elements like thyristor etc.
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