Question

Rod AB of radius 2r is joined with rod BC of radius r. They are of same material and are of same length. the combination carries a current I. Find relation between the potential difference through AB and BC


Ans: V(BC)=4V(AB)

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Answer 1

We know that,
Length of AB = l (say)
then,
Length of BC = l
Cross section Area of AB = π(2r)^2
=4πr^2
Cross section Area of BC = π r^2


Now,
Since, length and Material of rid is same, so
We know R is inversely proportional to Area of cross section.
R α 1/ A

Now,
V(AB)/V(BC) = I R(AB) / I R(BC)
= R(AB)/R(BC)
= A (BC) / A (AB)
= πr^2 / 4πr^2
= 1/4
=> 4V(AB) = V(BC)