Question

Eight copper wire of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2l$ have the same resistance $(R)$ then its diameter will be ______$d$.

Answer 1

Answer: 4

Each wire has resistance $=\rho \frac{4\ell }{\pi d^2}=r$
Eight wire in parallel, then equivalent resistance is $\frac{r}{8}=\frac{\rho \ell }{2\pi d^2}$
Single copper wire of length $2l$ has resistance
$R=\rho \frac{2\ell \times 4}{\pi d_1^2}=\frac{\rho \ell }{2\pi d^2}$
$\Rightarrow d_1=4d$