## A wire of given material having length l and area of cross-section Ahas a resistance of 4 β¦. 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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Examples from NCERT Book

Class 10

Chapter 12 Class 10 - Electricity (Term 2)

Last updated at Aug. 6, 2019 by Teachoo

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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 β¦. 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 = π π/π΄ where π = resistivity of the material l = length of the wire A = Area of cross-section of wire It is given that R = 4 Ξ© β΄ π π/π΄ = 4 Now, For the second wire Length of the wire = π2 = π/2 Area of cross β section = A2 = 2A Resistivity = π Finding resistance, R2 = π π_2/π΄_2 R2 = π (π/2) Γ 1/2π΄ (because the material is same) R2 = ππ/π΄ (1/2Γ1/2) R2 = ππ/π΄ (1/4) R2 = 4 Γ 1/4 R2 = 1 Ξ© Resistance of second wire is 1 Ξ©