Check sibling questions

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?

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Transcript

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 Ξ© ∴ 𝜌 𝑙/𝐴 = 4 Now, For the second wire Length of the wire = 𝑙2 = 𝑙/2 Area of cross βˆ’ section = A2 = 2A Resistivity = 𝜌 Finding resistance, R2 = 𝜌 𝑙_2/𝐴_2 R2 = 𝜌 (𝑙/2) Γ— 1/2𝐴 (because the material is same) R2 = πœŒπ‘™/𝐴 (1/2Γ—1/2) R2 = πœŒπ‘™/𝐴 (1/4) R2 = 4 Γ— 1/4 R2 = 1 Ξ© Resistance of second wire is 1 Ξ©

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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