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

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$8 / 9$

$1 / 3$

answer is D.

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Detailed Solution

$R = ρ \times \frac{l}{A}$

$\begin{array}{l} R = ρ \times \frac{l}{π r^{2}} \\ R α \frac{l}{r^{2}} \\ (\sin c e I α \frac{1}{R}) \end{array}$

$\Rightarrow \frac{i_{1}}{i_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} \times \frac{l_{2}}{l_{1}} = \frac{4}{9} \times \frac{3}{4} = \frac{1}{3}$

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