An electric current is passed through a circuit containing two wires of the same material, connected in…
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 $4 / 3$ and $2 / 3$, then the ratio of the currents passing through the wire will be
3
$1 / 3$
$8 / 9$
2
Solution
$
\frac{I_1}{I_2}=\frac{R_2}{R_1}
$
[current divider rule since voltage is same in parallel]
$
\begin{aligned}
& \frac{I_1}{I_2}=\frac{L_2}{L_1} \times \frac{r_1^2}{r_2^2} \\
& \therefore \frac{I_1}{I_2}=\frac{3}{4} \times\left(\frac{2}{3}\right)^2=\frac{1}{3} .
\end{aligned}
$