An electric of `5A` is passing through a circuit contaning three arrengement in parallel if the length and radius of the wires are in the ratio `2:3:4 and 3:4:5` then the ratio of current passing through wires should be

Options

A. `27:32:35`
B. `54:64:75`
C. `9:16:25`
D. `4:9:16`

Answer

b

Explanation

Given, `l_(1) :l_(2) :l_(3) = 2:3:4 = 2l:3l:4l`
`r_(1) :r_(2) :r_(3) := 3:4:5= 3r:4r:5r`
As resistance of wire, `R = (rho l)/(pir^(2))`
`:. R_(1) = (rho2l)/(pi(3r)^(2)) = (2)/(9)R, R_(2) = (rho 3l)/(pi(4r)^(2)) = (3)/(16)R,`
`R_(3) = (rho4l)/(pi(5r)^(2)) = (4)/(25)R`
`I_(1) = (V)/(R_(1)) : I _(2) = (V)/(R_(2)) : and I_(3) = (V)/(R_(3))`
`:. I_(1): I_(2): I_(3): (1)/(R_(1)): (1)/(R_(2)): (1)/(R_(3)) = (9)/(2R): (16)/(3R): (25)/(4R)`
`= (9)/(2):(16)/(3):(25)/(4)=54:64:75`