The resistance of a wire is inversely proportional to its area and directly proportional to its length. When the length is tripled then resistance will also become.

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Three times

One-third

Nine times

One-ninth

answer is A.

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Detailed Solution

Concept: It is important to remember that a wire's resistance is directly related to its length rather than being inversely proportional to its area. We can calculate the change in resistance by applying the formula,

R = ρl / A

Where, ρis the resistivity of the wire, L is the length of the wire and A is the cross sectional area of the wire.
That is, Resistance} =(Specific Resistivity Constant × Length of wire) } / Area of cross section of wire
RαL
So, if the length of the wire is tripled, the resistance will likewise increase by three times.
Rα1/A
In other words, when the wire is extended to three times its original length, its cross-section is reduced to one-third of its original cross-section. The aforementioned connection leads us to the conclusion that the present resistance is 9 times greater than the initial resistance.
Hence, option 1 is correct.

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