An electric current passes through a circuit containing two wires of the same material connected in parallel. If the lengths of the wires are in the ratio 4 3 and radius of the wires are in the ratio 2 3 , then the ratio of the current passing through the wires is m n , where m and n are smallest integers. What is m + n ?

Step-by-step solution

Given that, l 1 l 2 = 4 3 a n d r 1 r 2 = 2 3 Here, l 1 and l 2 are the length of the wires while r 1 and r 2 are the radii of the wires. Now, we know that V = I R ⟹ I R = c o n s t a n t ⟹ I 1 R 1 = I 2 R 2 o r       I 1 I 2 = R 2 R 1       … . i But we know that the resistance of the wire is                   R = ρ l A Hence, from Eq (i) I ⁡ 1 I ⁡ 2 = ρ l ⁡ 2 / A ⁡ 2 ρ l ⁡ 1