A wire of given material having length l and area of cross-section Ahas a resistance of 4 Ω. What would be the resistance of another wireof the same material having length l/2 and area of cross-section 2A?

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Example 12.6 A wire of given material having length l and area of cross-section A has a resistance of 4 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A?
We know that
Resistance of a wire = 𝜌 𝑙/𝐴
where
𝜌 = resistivity of the material
l = length of the wire
A = Area of cross-section of wire
It is given that R = 4 Ω
∴ 𝜌 𝑙/𝐴 = 4
Now,
For the second wire
Length of the wire = 𝑙2 = 𝑙/2
Area of cross − section = A2 = 2A
Resistivity = 𝜌
Finding resistance,
R2 = 𝜌 𝑙_2/𝐴_2
R2 = 𝜌 (𝑙/2) × 1/2𝐴
(because the material is same)
R2 = 𝜌𝑙/𝐴 (1/2×1/2)
R2 = 𝜌𝑙/𝐴 (1/4)
R2 = 4 × 1/4
R2 = 1 Ω
Resistance of second wire is 1 Ω

CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo

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