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NEETPhysicsCurrent Electricity

Two wires made of the same material and having the same length have their radii in the ratio 1:2 . If these two wires are connected in parallel across a battery, what will be the ratio of the currents flowing through them ( I₁ : I₂ )?

Options

  1. A1:2
  2. B2:1
  3. C4:1
  4. D1:4

Correct answer

D. 1:4

Step-by-step solution

The resistance of a wire is given by R = L A = L r^2 . Since the wires have the same material ( ) and length ( L ), their resistance is inversely proportional to the square of their radii: R₁ R₂ = ( r₂ r₁ )^2 Given the ratio of radii r₁ : r₂ = 1 : 2 , we have: R₁ R₂ = ( 2 1 )^2 = 4 1 When connected in parallel, the potential difference across both wires is the same. Therefore, the current is inversely proportional to the resistance ( I = V R ): I₁ I₂ = R₂ R₁ = 1 4 Thus, the ratio of the currents is 1:4 . Answer: 1:

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