Question

Two solid conductors are made up of same material, have same length and same resistance. One of them has a circular cross section of area A₁ and the other one has a square cross section of area A₂. The ratio A₁/A₂ is 

(1) 2 

(2) 1.5 

(3) 1 

(4) 0.8

Answer 1

Ans: (3) 1

Sol. Resistance of conductor is given as

$R={\rho l\over A}$

$\ \therefore\quad A={\rho l\over R}$

$\implies{A_1\over A_2}={\rho_1 \over \rho_2}\times{l_1 \over l_2}\left({R_2 \over R_1}\right)$

$\implies{A_1\over A_2}=1\quad$ [∵ R₁ = R₂, l₁ = l₂ and for same material $\rho_1=\rho_2$]