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. `3:6:10`
B. `4:9:16`
C. `9:16:25`
D. `54:64:75`

Answer

D

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`
Resistance of a wire, `R=(rhol)/(pir^(2))`
`R_(1)=(rho2l)/(pi(3r)^(2))=(2)/(9)(rhol)/(pir^(2))=(2)/(9)R, R_(2)=(rho3l)/(pi(4r)^(2))=(3)/(16)(rhol)/(pir^(2))=(3)/(16)R`
`R=(rho4l)/(pi(5r)^(2))=(4)/(25)(rhol)/(pir^(2))=(4)/(25)R`
`I_(1)=(V)/(R_(1)),I_(2)=(V)/(R_(2))andI_(3)=(V)/(R_(3))`
`therefore 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`