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 $\left(R\right)$ then its diameter will be $d.$

Answer 1

$R_{AB}=R$

$R=\frac{1}{8}($ Resistance of one wire $)$

$=\frac{1}{8}\rho \frac{l}{\pi \frac{d^2}{4}}=\frac{\rho l}{2\pi d^2}$

Resistance of copper wire of length $2l$ and diameter $x=R$.

$\rho \frac{2l}{\pi \frac{x^2}{4}}=R$

$\Rightarrow \frac{8\rho l}{\pi x^2}=\frac{\rho l}{2\pi d^2}$

$\Rightarrow 16d^2=x^2$

$\therefore x=4d$