Question

A wire of length l, area of cross section A and resistance R is stretched so that the

length is doubled. How will its resistance and resistivity change?​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Lenght of wire = $\ell$
• Cross section area of wire = A
• Resistance = R

Then ,

Lenght is doubled = 2$\ell$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Resistance (R)
• Resistivity ${\sf (\rho)}$

$\color{darkblue}\underline{\underline{\sf Solution-}}$

$\color{violet}\bullet\underline{\boxed{\sf R =\rho\dfrac{\ell}{A}}}$

Resistance is directly proportional to Lenght of wire

$\implies{\sf R\: \: \propto\:\:\ell}$

$\implies{\sf R \: \: \propto\:\;\dfrac{1}{A}}$

Therefore, if $\ell$ will be double then Resistance (R) will also doubled 2R

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Resistance will be doubled (2R)

Resistivity will be same because it's constant.

Answer 2

$\mathtt{\huge{ \fbox{Answer :)}}}$

As we know that ,

The resistance of the conductor is directly proportional to the length of the conductor & inversely proportional to its area of cross section

Thus ,

$\sf \hookrightarrow R ∝ \frac{ L}{A} \\ \\ \sf \hookrightarrow R = ρ\frac{ L}{A}$

Where , ρ is the constant of proportionality called resistivity

Now coming to your question ,

i) If the length of the wire is dubbled then the resistance will be doubled because

$\star$ $\sf R ∝ L$

ii) If the length of the wire is dubbled then the resistivity will be same because it is constant or the property of the material of the wire

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