CBSE Class 10 Answered
what is ohm's law? Derive it.
Asked by haritsourabhharit | 16 Oct, 2010, 09:22: AM
Expert Answer
Dear student
Following is the detailed account of arriving at Ohms law as an equation:
The sketch shows a conductor, length L, cross sectional area A. There are n charge carriers per cubic metre, each carrier having a charge q, and moving at an average speed v. The situation is analogous to the gravitational case except that we have charge q instead of mass m, and an electric field of magnitude E rather than a gravitational field of magnitude g. Inside the cylinder there are nAL charge carriers. The last charge carrier leaves the cylinder after a time t = L/v, so the total charge that leaves the cylinder per unit time is:
I = nAqv = n.A.const.E = const.V.nqA/L. (3)
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V/I = (L/A)(1/(nq.const.)), which we can write as
V/I = (L/A)ρ = R
Alternatively, we can take the reciprocal of the terms in the above equation and write:
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I/V = σ(A/L) = G
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σ = n.q.const = 1/ρ.
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J = σE = E/ρ.
This is also the form that is closest to the way in which Ohm expressed his eponymous law originally. The current is parallel to E so in this case the equation has been written in vector form.
We hope that clarifies your doubt
Regards
Team
TopperLearning
Answered by | 18 Oct, 2010, 12:29: PM
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