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

Options

A. `R_(A) = R_(B) = R_(C )`
B. `R_(A) gt R_(B) gt R_(C )`
C. `R_(A) lt R_(B) lt R_(C )`
D. Information is not sufficient

Answer

A

Explanation

(a) All the conductors have equal lengths. Area of cross section of `A` is `{(sqrt3 a)^(2) - (sqrt2 a)^(2)} = a^(2)`
Similarly area of cross-section of `B` = area of cross section of `C = a^(2)`
Hence according to formula `R = rho (l)/(A)`, resistance all the conductors are equal i.e., `R_(A) = R_(B) = R_(C)`