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  • Need explanation for: The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be :

The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be :

  • Option 1)

    nR

  • Option 2)

    \frac{\text{R}} {\text{n}}

  • Option 3)

    n2R

  • Option 4)

    \frac{\text{R}} {{\text{n}^\text{2} }}

 

Answers (1)

best_answer

As learnt in

Resistance formula -

R= ho frac{l}{A}=frac{m}{ne^{2} au}cdot frac{l}{A}

- wherein

ho = resistivity of material

n= Number of free electrons per unit volume.

 

 R = \rho \frac{1}{A}

R = \frac{\rho l^{2}}{Y} \Rightarrow R\:\alpha\: l^{2}

According to the question, l2 = nl1

\frac{R_{2}}{R_{1}}= \frac{n^{2}{l_{1}}^{2}}{{l_{1}}^{2}} = \frac{R_{2}}{R_{1}} = n^{2}

\Rightarrow R_{2}= n^{2}R_{1}

\because R_{1} = R\: and\:R_{2}= R^{1}

\therefore R^{1} =n^{2}R


Option 1)

nR

This answer is incorrect

Option 2)

\frac{\text{R}} {\text{n}}

This answer is incorrect

Option 3)

n2R

This answer is correct

Option 4)

\frac{\text{R}} {{\text{n}^\text{2} }}

This answer is incorrect

Posted by

prateek

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