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

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 $\Rightarrow \begin{aligned} & A_1 l_1=A \\ & \Rightarrow \frac{l_1}{l_2}=\frac{A_1}{A_2}\end{aligned}$
Now $\frac{R_1}{R_2}=\frac{l_1}{l_2} * \frac{A_2}{A_1}=\left(\frac{l_1}{l_2}\right)^2=\left(\frac{A_2}{A_1}\right)^2=\left(\frac{r_2}{r_1}\right)^4=\left(\frac{d_2}{d_1}\right)^4$
- If a wire of resistance R and length I is stretched to length nl, then new resistance of wire is $n^2 R$