Question

A cylindrical conductor of length 'l' and uniform area of cross section 'A' has resistance 'R' another conductor of length 2.5 l and resistance 0.5R of the same material has area of cross section...
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Answer 1

Answer:

Explanation: 5A

Answer 2

Given :

• For first conductor:

1. Length ( L₁) = l
2. Area of cross section (A₁) = A
3. Resistance (R₁) = R

• For second conductor:

1. Length ( L₂) = 2.5 l
2. Resistance (R₂) = 0.5 R

To find :

• Area of cross section of second conductor (A₂)

Solution :

• We know that, resistance of a conductor is given by,

       R = (ρL)/(A)       where ρ is the resistivity of the conductor.

•  ∴ ρ = (RA)/(L)

• The resisitivity of a given conductor depends only on the material of the conductor. We are given that both conductors have the same material. Hence , resistivity of both materials will be the same.

• ∴ ρ₁ = ρ₂

        ∴ (R₁.A₁)/L₁ = (R₂.A₂)/L₂

        ∴ (R.A)/l = (0.5R × A₂)/2.5l

• ∴ A₂ = 5A

Answer : The area of cross section of the second conductor will be 5A.