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 $2 l$ have the same resistance $(R)$ then its diameter will be ______$d$.

Answer 1

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 $2 l$ has resistance
$ R =\rho \frac{2 \ell \times 4}{\pi d _1^2}=\frac{\rho \ell}{2 \pi d ^2}$
$ \Rightarrow d _1=4 d$