A wire of given material having length l and area of cross-section A has a resistance of 4 โ„ฆ. 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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  1. Class 10
  2. Chapter 12 Class 10 - Electricity

Transcript

Example 12.6 A wire of given material having length l and area of cross-section A has a resistance of 4 โ„ฆ. 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 = ๐œŒ ๐‘™/๐ด where ๐œŒ = resistivity of the material l = length of the wire A = Area of cross-section of wire It is given that R = 4 ฮฉ โˆด ๐œŒ ๐‘™/๐ด = 4 Now, For the second wire Length of the wire = ๐‘™2 = ๐‘™/2 Area of cross โˆ’ section = A2 = 2A Resistivity = ๐œŒ Finding resistance, R2 = ๐œŒ ๐‘™_2/๐ด_2 R2 = ๐œŒ (๐‘™/2) ร— 1/2๐ด (because the material is same) R2 = ๐œŒ๐‘™/๐ด (1/2ร—1/2) R2 = ๐œŒ๐‘™/๐ด (1/4) R2 = 4 ร— 1/4 R2 = 1 ฮฉ Resistance of second wire is 1 ฮฉ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.