state ohms law. derive the relation and give graphical representation for it. urgrnt pl urgent pl

Asked by aahlad06 | 9th Jan, 2018, 07:55: PM

Expert Answer:

In a conducting material, electron's drift speed depends on electric field E. Since the current density also depends on drift speed, we can consider that current density J is proportional to electric Field E. The proportionality constant σ is called conductivity of the material. The relation between current density J and electric field is given by
J = σE ...........................(1)
current density J = i / A, where i is the current flowing through the conductor and  A is area of cross section.
If there is a potential difference of ΔV volts across a length l of conductor, then electric field E = .ΔV / d ( units V/m)
normally conductivity σ is given in terms of resistivity ρ of the material and they are related as σ = 1 / ρ.
by substituting for j, E and σ in equation (1 ), we get
begin mathsize 12px style i over A space equals space 1 over rho fraction numerator capital delta V over denominator l end fraction h e n c e space capital delta V space equals space fraction numerator rho l over denominator A end fraction space i h e r e space fraction numerator begin display style rho l end style over denominator begin display style A end style end fraction space i s space t h e space r e s i s tan c e space space R space o f space c o n d u c t o r h e n c e space space capital delta V space equals space R cross times space i end style
Statement of Ohm's law:-
Potential difference across a conductor is the product of resistance and current flowing through it

Answered by Thiyagarajan K | 9th Jan, 2018, 09:57: PM

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