Question

Following figure shows cross-sections through three long conductors of the same length and material, with square cross-section of edge lengths as shown. Conductor B will fit snugly within conductor A, and conductor C will fit snugly within conductor B. Relationship between their end to end resistance is

• A. $R_A=R_B=R_C$
• B. $R_A>R_B>R_C$
• C. $R_A<R_B<R$
• D. Information is not sufficient

Answer 1

The correct option is A $R_A=R_B=R_C$

All the conductors have equal lengths. Area of cross-section of A is $\left\{\right(\sqrt{3}a{)}^2-\left(\sqrt{2}a{)}^2\right\}=a^2$
Similarly area of cross-section of B - Area of cross-section of $C=a^2$
Hence according to formula $R=\rho \frac{l}{A}$; resistances of all the conductors are equal i.e. $R_A=R_B=R_C$