Question

A wire has a resistance of 8 ohms. A second wire is half the length of the first wire and twice its diameter. What is the resistance of second wire?

Answer 1

\[R_1=\rho\frac{l_1}{S_1}\quad,\quad R_2=\rho\frac{l_2}{S_2}\]\[\frac{R_2}{R_1}=\frac{\rho l_2/S_2}{\rho l_1/S_1}=\frac{l_2}{l_1}\frac{S_1}{S_2}\quad;\quad l_2=l_1/2\quad,\quad S_2=4S_1\]\[R_2=R_1\frac{l_1/2}{l_1}\frac{S_1}{4S_1}=\frac{R_1}{8}=1\Omega\]

Answer 2

Could you please explain how you got 4S1? I know the questions says twice the diameter, but how do we get 4S1?

Answer 3

\[S=\pi r^2=\pi d^2/4\]