A cylindrical conductor of length ‘l’ and uniform area of cross section ‘A’ has resistance ‘R’. The area of cross section of another conductor of same material and same resistance but of length ‘2l’ is

Extra Question A cylindrical conductor of length l and uniform area of cross section A has resistance R. Another conductor of length 2l and resistance R of the same material has area of cross section (a) A/2 (b) 3A/2 (c) 2 A (d) 3 AGiven
Length of the conductor = l
Area of cross-section = A
Resistance of the conductor = R
Let the resistivity of the conductor = 𝜌
We know that,
R = 𝜌 𝑙/𝐴
∴ A = 𝜌𝑙/𝑅
New Conductor
Given,
Length of other conductor = l2 = 2l
Resistance of the conductor = R
Since the material is same,
Resistivity of the conductor = 𝜌
Now,
R = 𝜌 𝑙_2/𝐴_2
R = 𝜌 (2l) × 1/𝐴_2
A2 = (𝜌 (2𝑙))/𝑅
A2 = 2((𝜌 𝑙)/𝑅)
A2 = 2 A
∴ (c) is correct

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 12 years and a teacher from the past 16 years. He teaches Science, Accounts and English at Teachoo