A certain wire A has resistance 81 . The resistance of another wire of same material and equal length but of diameter thrice the diameter of will be [2023]

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Solution

Q.
A certain wire A has resistance 81 $Ω$ . The resistance of another wire $B$ of same material and equal length but of diameter thrice the diameter of $A$ will be [2023]

1 81 $Ω$

2 9 $Ω$

3 729 $Ω$

4 243 $Ω$

Ans.
(2)

Let wire $A$ have cross sectional area $A$ , radius $r$ , length $l$ and diameter $d$ .

$R \to$ Resistance of wire

For wire B : $L' = L;$ $d' = 3 d;$ $r' = 3 r$

Area, $A' = 9 A$

As, $R = \frac{ρ L}{A} and R' = \frac{ρ L'}{A'} = \frac{ρ L}{9 A} = \frac{R}{9}$

Given : $R = 81 Ω,$ $R' = \frac{81 Ω}{9} = 9 Ω$

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