1
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Question

# Two metallic wires A and B are connected in series Wire A has length l and radius r while wire B has length 2l and radius 2r If both the wires are of same material then and the ratio of the total resistance of series combination to the resistance of the wire A

A
34
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B
32
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C
62
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D
65
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Solution

## The correct option is A 32Let the resistivity of both the wires be 'ρ'.The resistance of the wire A is given as RA=ρlπr2.The resistance of the wire B is given as RB=ρ2lπ2r2 = ρl2πr2.Now when the resistance are connected in seires is R=RA+RB. That is, R=32(ρlπr2).So, the required ratio is R:RA=32(ρlπr2):qlπr2.Therefore, R:RA=3:2.Hence, the ratio of the resistances in series and only wire A is 3/2.

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