Change Of Resistance In Wires By Stretching MCQ

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Stretching of wire

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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