A cylindrical metal rod of length L and diameter D is connected across a battery

Question

A cylindrical metal rod of length L and diameter D is connected across a battery having no internal resistance. An ammeter in the circuit measures the current to be I. If we now double the diameter of the rod, but change nothing else, the ammeter will read: A. 4I B. 2I C. I/2 D. I/4 A cylindrical metal rod of length L and diameter D is connected across a battery having no internal resistance. An ammeter in the circuit measures the current to be I. If we now double the diameter of the rod, but change nothing else, the ammeter will read: A. 4I B. 2I C. I/2 D. I/4 C. I/2 D. I/4

Explanation / Answer

   Resistance   R   =   ? * l / A   =   4 * ? * l / D2    where   D   =   diameter of wire    R   =   4 * ? * l / D2    On doubling diameter    R'   =   4 * ? * l / (2D)2          =    ? * l / D2          =   R / 4          =   R / 4    Initial current   I   =   V / R    Final current   I'   =   V / R'                               =   4 * V / R                               =   4 * I    A.   4 I      

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