# Two solid conductors are made up of same material, have same length and same resistance. One of them has a circular

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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

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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 $\rho_1=\rho_2$]