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.

 

V-I Graph:

 

On comparing V = RI with y = mx, we conclude that-

• The graph between V (plotted on Y-axis) and I (plotted on X-axis) is a straight line passing through origin.
• The slope of V-I graph = resistance of conductor.

 

 

I-V 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 Y-axis) and V (plotted on X-axis) is a straight line passing through origin.
• The slope of I-V 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-

 

(Equation-01)

 

Also,  we know the resistance of a conductor having length L & area of cross-section A is given by-

 

(Equation-02)

 

Substituting Equations-01 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 Non-Ohmic Conductors-

 

Ohm’s law is obeyed by many substances under certain conditions but it is not a fundamental law of nature.

 

Ohmic Conductors	Non-Ohmic Conductors
Ohmic conductors are those which obey Ohm’s law.	Non-ohmic conductors are those which do not obey Ohm’s law.
The resistance of ohmic conductors is constant at a given temperature.	The resistance of non-ohmic 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 non-ohmic conductors, situations may be of types- Straight line V-I graph not passing through origin V-I relationship is non-linear etc
Examples of ohmic conductors- copper, silver etc.	Examples of non-ohmic conductors- p-n 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 non-linear elements like thyristor etc.

 

Test Your Concepts-

Quiz on Ohm’s Law

 

Next Article-

Kirchhoff’s Laws

 

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