Question

If length of a metallic wire becomes n times,
its resistance becomes
(a)
${n}^{2}$
n times (b)
$\sqrt{n}$
times
(c)
$\frac{1}{ \sqrt{n} }$
times
(d)
$\frac{1}{ {n}^{2} }$
times
​

Answer 1

Answer:

Answer -

Option A is the correct answer .

Solution -

Suppose that the initial length of the metallic wire is x units.

Now, the length of the metallic wire is stretched by n times.

Hence the new length of the wire becomes nx units .

Now,  Resistance is directly proportional to the length of the wire and is inversely proportional to the cross sectional area.

So, from the above statement , we can state that  length is inversely proportional to the cross sectional area.

So, the product of the length and the cross sectional area of any wire is a constant .

Using this,

x.A = nx NA

So, NA = n times less than original area .

So. nX / NA = n^2.

This is the required answer .

Hence, option A is correct .

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