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Question
A metal rod of length 10 cm and a rectangular cross-section of 1 cm × `1/2` cm is connected to a battery across opposite faces. The resistance will be ______.
Options
maximum when the battery is connected across 1 cm × `1/2` cm faces.
maximum when the battery is connected across 10 cm × `1/2` cm faces.
maximum when the battery is connected across 10 cm × `1/2` cm faces.
same irrespective of the three faces.
Solution
A metal rod of length 10 cm and a rectangular cross-section of 1 cm × `1/2` cm is connected to a battery across opposite faces. The resistance will be maximum when the battery is connected across 1 cm × `1/2` cm faces.
Explanation:
The resistance of a wire depends on various parameters, its area, material (resistivity) and length (length of the rod).
Here, the metallic rod behaves as a wire.
The relationship between resistance and various parameter is given by R = ρl/A.
The resistance of a wire is given by R = `p l/A`
For greater value of R, l must be higher and A should be lower and it is possible only when the battery is connected across 1 cm × `(1/2)` cm (area of corss-section A).
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