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Question
A metal rod of square cross-sectional area A having length l has current I flowing through it when a potential difference of V volt is applied across its ends (figure I). Now the rod is cut parallel to its length into two identical pieces and joined as shown in figure II. What potential difference must be maintained across the length of 2l. so that the current in the rod is still I?
Solution
From Ohm's law, we have
\[V = IR\]
\[ \Rightarrow V = I\rho\frac{l}{A} . . . . . (1)\]
When the rod is cut parallel, and rejoined by length, the length of the conductor becomes 2l, whereas the area decrease to
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