There are two wires, A and B, made of same material. Both the wires have the same length. It is observed that the resistance of wire A is four times the resistance of wire B, then find the ratio of their cross sectional areas.

4 : 1

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1 : 4

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1 : 2

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2 : 1

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Solution

The correct option is B $1 : 4$
We know that $R = \frac{ρ \times l}{A}$
Given the material of both wires A and B is same and their lengths are also given to be same. $ρ a n d l$ are constant.
So, we have the relation:
$\frac{R_{A}}{R_{B}} = \frac{A_{B}}{A_{A}} = \frac{4}{1}$
So, $\frac{A_{A}}{A_{B}} = \frac{1}{4}$

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There are two wires, A and B, made of same material. Both the wires have the same length. It is observed that the resistance of wire A is four times the resistance of wire B, then find the ratio of their cross sectional areas.

The correct option is B 1:4We know that R=ρ×lAGiven the material of both wires A and B is same and their lengths are also given to be same. ρandl are constant.So, we have the relation:RARB=ABAA=41So, AAAB=14