Question

A wire of resistance $10\Omega$ is stretched such that its radius becomes half while it's volume remains constant. What will be the new resistance?

• A. $160\Omega$
• B. $140\Omega$
• C. $120\Omega$
• D. $100\Omega$

Answer 1

The correct option is A $160\Omega$

When we change the radius of a wire without changing it's volume then:
$\frac{R_1}{R_2}=(\frac{r_2}{r_1}{)}^4\Rightarrow \frac{10}{R_2}=(\frac{\frac{r}{2}}{r}{)}^4=\frac{1}{16}$
$\frac{10}{R_2}=\frac{1}{16}\Rightarrow R_2=160\Omega$