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

Options

A. `2:3`
B. `3:2`
C. `8:27`
D. `27:8`

Answer

C

Explanation

Given `(i_(1))/(l_(2))=(2)/(2)(r_(1))/(r_(2))=(2)/(3)`

In order to solve this we have to look at the wires from the perspective of resistance.
`(R_(1))/(R_(2))=rho(I_(1))/(pir_(1)^(2)) (pir_(2)^(2))/(rho l_(2))=(I_(1))/(I_(2)) ((mu_(2))/(mu_(1)))^(2)`
`=(3)/(2)((3)/(2))^(2)=(27)/(8)`
Hence, the resistances are in a ratio of `(27)/(8)` . Since current distribution is inversely proportional to resistance hence, ratio of currents will be `(27)/(8)`