Question

A copper wire of certain length has a resistance of 10 ohms what will be its resistance after stretching to double its length

Answer 1

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

• Let the Lenght of copper wire is = $\ell$
• Resistance (R) = 10 Ω

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

• Resistance after stretching to double its Lenght ${\sf 2\ell}$

★$\color{darkblue}\underline{\underline{\sf Formula \: Used -}}$

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

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

$\implies{\sf R=\rho\dfrac{\ell}{A} }$

From here we can see that -

$\color{indigo}{\sf R \: \propto \: \ell}$

Resistance is directly proportional to Lenght of wire

$\color{indigo}{\sf R \: \propto \: \dfrac{1}{A}}$

Resistance is inveresly proportional Cross section area

Resistance = 10Ω (Given )

If Lenght will double then Resistance will also Double

${\sf \therefore \: R_2=2×10 }$

$\color{red}{\sf R_2=20Ω}$

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

Resistance after stretching Lenght to double will be $\color{red}{\sf 20Ω}$