Question

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

• A. 3
• B. 44564
• C. 44782
• D. 2

Answer 1

Answer: (B)

44564

Answer 2

$\frac{I_{1}}{I_{2}} = \frac{R_{2}}{R_{1}}$ [current divider rule since voltage is same in parallel] $\frac{I_{1}}{I_{2}} = \frac{L_{2}}{L_{1}}\times\frac{r^{2}_{1}}{r^{2}_{2}}$ $\therefore \frac{I_{1}}{I_{2}} = \frac{3}{4}\times\left(\frac{2}{3}\right)^{2} = \frac{1}{3}.$