Two wires of the same material having lengths and radii in the ratio of 3:4 and 3:2 respectively are connected in parallel with a potential source of 6 V. The ratio of currents flowing through them, I₁ : I₂ = _.

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(2) 3:1. Given: ℓ₁ : ℓ₂ = 3 : 4, r₁ : r₂ = 3 : 2, same material, the same 6 V across both (parallel). R = (ρℓ)/(π r²), so (R₁)/(R₂) = (ℓ₁)/(ℓ₂)((r₂)/(r₁))² = 3/4×4/9 = 1/3. In parallel the voltage is the same, so I ∝ 1/R and (I₁)/(I₂) = (R₂)/(R₁) = 3. So I₁ : I₂ = 3 : 1. The value 6 V is not needed for the ratio.

Two wires of the same material having lengths and radii in the ratio of 3:4 and 3:2 respectively are connected in parallel with a potential source of 6 V. The ratio of currents flowing through them, I₁ : I₂ = _______.

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