An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If lengths and radii of the wires are in the ratio of 4 : 3 and 2 : 3 , then ratio of the currents passing through the wires will be

Options

A. `3:1`
B. `2:1`
C. `1:3`
D. `1:2`

Answer

C

Explanation

Given : Length of first wires `(l_(1)) = 4 l,`
Length of second wire `l_(2) = 3l,`
Radius of first wire `(r_(1)) = 2 r ` and
Radius of second wire `(r_(2)) = 3r `
`(R) = p xx (l)/(A) = p xx (l)/(pir^(2))prop (1)/(r^(2))`
`:.(R_(1))/(R_(2)) =(l_(1))/(l_(2)) xx ((r_(2))/r_(1))^(2) = (4l)/(3l)xx((3r)/(2r))^(2)`
`= (4)/(3) xx (9)/(4) = 3 (or) R_(1) = 3 R_(2)`
Since both the wires are connected in parallel therefore potential difference -(V) across the wires will be the same . We also know that
Current in the wire `(I) = (V)/(R) prop (1)/(R)`
`:. (l_(1))/(l_(2)) = (R_(2))/(R_(1)) = (R_(2))/(3R_(2)) = (1)/(3)` (or)
`I_(1): I_(2) = 1 : 3 `