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

Each wire has resistance=ρ $\frac{4l}{\pi d^2}$=r
Eight wires in parallel, then equivalent resistance is $\frac{r}{8}$=$\frac{\rho l}{2\pi d^2}$
Single copper wire of length 2l has resistance
R=ρ $\frac{2l\times4}{\pi d_1^2}$=$\frac{\rho l}{2\pi d^2}$
⇒d1=4d