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Change Of Resistance In Wires By Stretching - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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• 12 Questions around this concept.

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The resistance of a wire is $5\Omega$ . It's new resistance in ohm if stretched to $5$ times of its original length will be :

Concepts Covered - 1

Stretching of wire
1. Stretching of wire

If a conducting wire stretches its length increases area of cross-section decreases but volume remains constant

Suppose for a conducting wire before stretching

it’s length = $l_1$, area of cross-section =$A_1$, radius =$r_1$, diameter = $d_1$,

and resistance  $R_1=\rho \frac{l_1}{A_1}$

After stretching length =$l_2$, area of cross-section =$A_2$, radius = $r_2$, diameter = $d_2$

and resistance  $R_2=\rho \frac{l_2}{A_2}$

So $\frac{R_1}{R_2}=\frac{l_1}{l_2}*\frac{A_2}{A_1}$

But Volume is constant So $A_1l_1=A_2l_2\\ \Rightarrow \frac{l_1}{l_2}=\frac{A_1}{A_2}$

Now $\frac{R_1}{R_2}=\frac{l_1}{l_2}*\frac{A_2}{A_1}=(\frac{l_1}{l_2})^2=(\frac{A_2}{A_1})^2=(\frac{r_2}{r_1})^4=(\frac{d_2}{d_1})^4$

• If a wire of resistance R and length l  is stretched to length nl, then new resistance of wire is $n^2R$

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Stretching of wire

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