Two wires of same material having lengths and radii in the ratio of 3 : 4 and 3 : 2 respectively are connected in parallel with a potential source of 6V.
the ratio of currents flowing through them `I_(1) : I_(2) ` = ..... .

Options

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

Answer

C

Explanation

` 3: 1`
`R = (rho l)/(A) = (rho l)/(pi r^(2))`
`therefore R prop (l)/(r^(2))`
` therefore (R_(1))/(R_(2)) = (l_(1))/(l_(2)) xx ((r_(2))/(r_(1)))^(2) `
`therefore (R_(2))/(R_(1)) = (l_(2))/(l_(1)) xx ((r_(1))/(r_(2)))^(2) " " `... (1)
But V `I_(1) R_(1) = I_(2) R_(2) `
`therefore (I_(1))/(I_(2)) = (R_(2))/(R_(1))`....(2)
From equation (1) and (2).
`(I_(1))/(I_(2)) = (4)/(3) xx ((3)/(2))^(2) = (4)/(3) xx (9)/(4) = (3)/(1)`