    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:√7From 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 V∝lr2 ⟹V1V2=l1l2×(r2)2(r1)2 ⟹r1r2=√V2×l1V1×l2 = √3.6×24.2×3 = 2√7.  Suggest Corrections  3      Similar questions  Related Videos   Ohm's Law in Scalar Form
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