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  • An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and the radii of the wires are in the ratio of <img alt="\frac{4}{3}

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

Option: 1

3


Option: 2

\frac{1}{3}


Option: 3

\frac{8}{9}


Option: 4

2


Answers (1)

best_answer

\begin{aligned} &\mathrm{ \frac{I_1}{I_2}=\frac{R_2}{R_1}, \frac{I_1}{I_2}=\frac{\rho L_2}{A_2} \times \frac{A_1}{\rho L_1} }\\ &\mathrm{ \text { Or } \frac{I_1}{I_2}=\left(\frac{L_2}{L_1}\right)\left(\frac{A_1}{A_2}\right) \text { or } \frac{I_1}{I_2}=\left(\frac{L_2}{L_1}\right)\left(\frac{\pi r_1^2}{\pi r_2^2}\right) }\\ &\mathrm{ =\frac{L_2 r_1^2}{L_1 r_2^2}=\frac{3}{4}\left(\frac{2}{3}\right)^2=\frac{3}{4} \times \frac{4}{9}=\frac{1}{3}}\\ \end{aligned}

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