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Question

Two wires of the same material having lengths in the ratio 2:3, are connected in series. The potential differences across the wires are 4.2V and 3.6V respectively. The ratio of their radii would be:

A
2:7
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B
7:2
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C
2:7
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D
7:2
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Solution

The correct option is A 2:7
From Ohm's law, we know that potential difference V=iR, where i is the current flowing and R is the resistance of the wire given by R=ρlA

ρ is the specific resistance of the material which is a constant in this case as the two wires are of the same material.
A is the area of the cross section of the wire = πr2, r is the radius of the cross section of the wire.

Given, voltages V1=4.2V and V2=3.6V
Ratio of lengths = l1:l2=2:3

We have Vlr2
V1V2=l1l2×(r2)2(r1)2
r1r2=V2×l1V1×l2 = 3.6×24.2×3 = 27.

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