Change Of Resistance In Wires By Stretching MCQ - Practice Questions with Answers

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 $=d_1$,

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

and resistance
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}
$

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

But Volume is constant So $\Rightarrow \frac{A_1 l_1=A_1}{l_2}=\frac{A_1}{A_2}$
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 $n^2 R$