Question

a given wire is double its length. how will its resistance and resistivity change​

Answer 1

here is your answer ...

we know that the resistance of a conductor is directly proportional to its length .

so if the given wire is double its length then its resistance will also get doubled .

resistivity will have no effect due to the length .

hope this will help you .

##follw me##

Answer 2

Resistance is directly proportional to its length. In a mathematical way,

R ∝ length/Area

Here, area refers to cross section area. When we say any two quantities are directly proportional then it means that if one quantity will increase/decrease then other quantity will also increase/decrease in same order.

Length has no connection with resistivity. If the material remains same then resistivity wil remain unchanged.

R₁ = p × l₁ / A

R₂ = p × l₂ / A

R₁ / R₂ will be

$\Longrightarrow \bold{\frac{ p \times l_1}{A} \times \frac{A}{ p \times l_2}} \\ \\ \Longrightarrow \bold{ \frac{ p \times l_1}{A} \times \frac{A}{ p \times 2l_1}}$

R₁ / R₂ = 1 / 2 Or

R₂ = 2 × R₁

Thus, our new resistance wil be twice of older one.

( Note : This is possible when cross section area and resistivity will be equal )

R₂ = 2 R₁