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# An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of $\large\frac{4}{3} \: and \:\large\frac{2}{3}$, then the ratio of the currents passing through the wires will be

$\begin {array} {1 1} (A)\;3 & \quad (B)\;\large\frac{1}{3} \\ (C)\;\large\frac{8}{9} & \quad (D)\;2 \end {array}$

$\large\frac{I_1}{I_2}$ $= \large\frac{R_2}{R_1}$
[ Current divider rule since voltage is same in parallel ]
$\large\frac{I_1}{I_2}$ $= \large\frac{L_2}{L_1}$ $\times \large\frac{r_1^2}{r_2^2}$
$\therefore \large\frac{I_1}{I_2}$ $= \large\frac{3}{4}$ $\times \bigg( \large\frac{2}{3} \bigg)^2$ $= \large\frac{1}{3}$
Ans : (B)

edited Mar 14, 2014