Two wires of same material have their lengths in the ratio 2:3 and radii 8:9 . Equal value of p.d is applied between their ends (separately). Calculate the ratio of current through those two

Explanation

We know that `R= (rhol)/(A) =(rhol)/(pir^2)`
`R= (rhol)/(pir^2)`
Substitute `R= V/I`
`V/I =(rhol)/(pir^2) implies I = (Vpir^2)/(rhol)`
`I prop (r^2)/(l)`
`(I_1)/(I_2) =(r_1^2)/(l_1) xx(l_2)/(r_2^2)`
`(I_1)/(I_2) =(r_1^2)/(r_2^2) xx ((l_2)/(l_1)) = (8^2 xx 3)/(9^2 xx 2) =(64xx3)/(81xx2) = (32)/(27)`
`I_1 :I_2 =32:27`