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Question: Following figure shows cross-sections through three long conductors of the same length and material,...

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

RA = RB = RC

B

RA>RB>RC

C

RA<RB<R

D

Information is not sufficient

Answer

RA = RB = RC

Explanation

Solution

All the conductors have equal lengths. Area of cross-section of A is {(3a)2−(2a)2}=a2\left\{ (\sqrt{3}a)^{2} - (\sqrt{2}a)^{2} \right\} = a^{2}

Similarly area of cross-section of B = Area of cross-section of C = a2

Hence according to formula R=ρlA;R = \rho\frac{l}{A}; resistances of all the conductors are equal i.e. RA = RB = RC