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Is it true that the resistance of a wire becomes two times the original resistance when the wire is stretched to double its length?

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True

False

answer is B.

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Detailed Solution

The above statement is False.
We know that

R α l,

where R is resistance and l is length of wire. Now consider R be the original resistance of the wire and

l

be the length and A be the area of the cross section of wire. Then resistance of wire can be expressed as-

R = \frac{ρl}{A}

………….(i); Where,

ρ

is the resistivity of the wire.
When we stretch the wire its length becomes double and area of cross section reduced. So, length of new wire

(l^{'} = 2 l)

…………… (ii)
area of cross section

(A^{'} = \frac{A}{2})

…………….. (iii)
Then resistance of new wire (

R^{'}

) can be written as,

R^{'} = \frac{ρ l^{'}}{A^{'}}

…………………… (iv) Put the values of equation (ii) and (iii) in (iv)

R^{'} = \frac{ρ \times 2 l}{{\frac{A}{2}}^{}}

ⴾ

R^{'} = \frac{2 \times ρ \times 2 l}{A^{}}

ⴾ

R^{'} = \frac{4 \times ρ l}{A^{}}

………………(v)
Comparing equation (i) and (v) we can say,

R^{'} = 4 R

The corrected statement would be the resistance of a wire becomes four times the original resistance when wire is stretched to double its length.

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