Question

Two metal wires have the resistivity 1.62 × 10-8 ohm meter and 4.68 × 10-8 ohm meter .Comapre the resistance if A is twice long as B and half of its diameter

Answer 1

resistivity of wire A , $\rho_A$ = 1.62 × 10^-8 ohm. m
resistivity of wire B , $\rho_B$ = 4.68 × 10^-8 ohm . m
Let length of wire B is l
then, length of wire A will be 2l
similarly , Let's assume that diameter of wire A is d
then, diameter of wire B will be 2d.

we know, $R=\rho\frac{l}{a}$
where R is resistance, $\rho$ is resistivity, l is the length of the wire and a is cross sectional area.

so, resistance of wire A , $R_A=1.62\times10^{-8}\frac{2l}{\pi d^2/4}$

and resistance of wire B, $R_B=4.68\times10^{-8}\frac{l}{\pi (2d)^2/4}$

$\frac{R_A}{R_B}=\frac{1.62\times8}{4.68}$

$\frac{R_A}{R_B}=\frac{36}{13}$

Answer 2

Check the ans in this attachment