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A piece of wire with a resistance $R$ is drawn to double its length. What will be the new resistance?

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R

2 R

4 R

\frac{R}{4}

answer is C.

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Detailed Solution

A piece of wire with a resistance

R

is drawn to double its length. Its new resistance will be

4 R

.
A wire of resistance

R

is given.
It is known that “the resistance

(R)

of the wire is directly proportional length

(l)

of the wire and the resistivity

(ρ)

of the material. It is inversely proportional to the area of the cross-section

(A)

.” Mathematically,

R = ρ \frac{l}{A} (i)

Since the length is doubled, new length

(L)

is equal to

L = 2 l

Since the volume of the wire is constant,

\Rightarrow Al = A' 2 l

Therefore, the new cross sectional area of the wire is,

\Rightarrow

A ’ = \frac{A}{2}

Substituting the value of new length in the relation, we get

\Rightarrow R' = ρ \frac{2 l}{A / 2} (ii)

From

(ii)

and

(ii)

, it can be concluded that

\Rightarrow R ’ = 4 R

Hence, the resistance becomes four times the initial resistance.

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