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 0-5 R
of the same material has area of cross-section
(A) 5A
(B) 2.5 A
0-5 A
(D)1/5 A
​

Answer 1

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. Hence option (A) is correct.

Answer 2

Answer:

Option (A) 5A.

Explanation:

Two cylindrical conductor with same material, so the value will be directly proportional to it.

1st Cylinder

Length - l

Resistance - R

Cross-section - A

R = pl/A

A= pl/R    [equation (i)]

2nd Cylinder

l = 2.5 l

R = 0.5 R

A = ?

R = pl/A  (p= resistivity constant = 1)

0.5 = 1*2.5/A    [equation (ii)]

A= 5A

Comparing equation (i) & (ii) -

i = ii

pl/R = p*2.5l/0.5R

A = 5A

Hence, proved.

Two cylindrical conductor of same material have length, cross-section area and resistance - l, A, R and length - 2.5l, cross-section area - A and Resistance - 5R.

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