Question

A cylindrical conductor of length 'L' and uniform area of cross section a has resistance 'R'. Another conductor of length 2.5L and resistance 0.5R are of the same material has area of cross section

A) 5A
B) 2.5A
C) 0.5A
D) 1/5
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Answer 1

Answer:

5A

Explanation:

Answer 2

Given :

• Length of first conductor L₁ = L
• Length of second conductor L₂ = 2.5L
• Resistance of first conductor R₁= R
• Resistance of second conductor R₂= 0.5R
• Area of cross section of first conductor A₁= A

To find :

• Area of cross section of second conductor A₂

Solution :

• The material of both the conductors is the same. Hence their resisitivity(ρ) will be the same, as resisitivity depends only on the material of the conductor.
• ∴ ρ₁ = ρ₂    ....(1)
• We know that, resistance of a conductor is given by,

       R = (ρL)/(A)    

      ∴ ρ = (RA)/(L)

• Substituting the value of ρ in equation (1),

        (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 is 5A. So the option (A) is correct.