Q. 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) $R_{A} < R_{B} < R_{C}$
D) Information is not sufficient
Explanation
(a) All the conductors have equal lengths. Area of cross-section of $A$ is $\left\{ \left( \sqrt{3}a \right)^{2} - \left( \sqrt{2}a \right)^{2} \right\} = a^{2}$
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 $i.e.\ R_{A} = R_{B} = R_{C}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.