Question

Two different wires have specific resistivities, lengths and areas of cross-section in the ratio 3:4, 2:9 and 8:27 respectively. Find the ratio of resistances of the two wires.

Answer 1

We know that resistance, $R=\frac{\rho L}{A}$
where $\rho$ is the resistivity, L is the length and A is the area of cross-section.
Now, $\frac{R_1}{R_2}=\frac{\left(\frac{{\rho }_1{L}_1}{A_1}\right)}{\left(\frac{{\rho }_2{L}_2}{A_2}\right)}=\frac{\left(\frac{3\times 2}{8}\right)}{\left(\frac{4\times 9}{27}\right)}=\frac{\frac{3}{4}}{\frac{4}{3}}=\frac{9}{16}$