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 - Physics MCQ AIEEE 2004 2026 | ExamTest.live

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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 wires will be:

Solution & Step-by-step Explanation

In parallel, voltage V is same. I = V / R ⟹ I \propto 1/ R . R = ρ \frac{L}{A} = ρ \frac{L}{π r ^{2}} \propto \frac{L}{r ^{2}} .So, I \propto \frac{r ^{2}}{L} . \frac{I _{1}}{I _{2}} = \frac{r _{1}^{2} / L _{1}}{r _{2}^{2} / L _{2}} = (\frac{r _{1}}{r _{2}})^{2} \times \frac{L _{2}}{L _{1}} Given \frac{L _{1}}{L _{2}} = \frac{4}{3} and \frac{r _{1}}{r _{2}} = \frac{2}{3} : \frac{I _{1}}{I _{2}} = (\frac{2}{3})^{2} \times (\frac{3}{4}) = \frac{4}{9} \times \frac{3}{4} = \frac{3}{9} = \frac{1}{3}

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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 wires will be:

3

1/3

8/9

2

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