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

1 : 3

The correct answer is Option (2) → 1 : 3

The resistance (R) of a given wire is -

$R=ρ\frac{L}{A}$

∴ Ratio of Resistance,

$\frac{R_1}{R_2}=\frac{ρ\frac{L_1}{\pi {r_1}^2}}{ρ\frac{L_2}{\pi {r_2}^2}}=\frac{L_1}{L_2}×\frac{{r_1}^2}{{r_2}^2}$

$=\frac{4}{3}×\frac{(3)^2}{(2)^2}=\frac{1}{3}$