Three resistances 2R, 3R and 6R of same material and same length having area of cross-section in ratio
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Given : Three resistances 2R, 3R and 6R of same material and same length
To find : ratio of their area of cross-section
Solution:
R = ρ L/A
ρ - same as same material
L is same as length is same
Let say area of cross sections are A₁ , A₂ and A₃ for resistances 2R, 3R and 6R respectively
2R = ρ L/A₁
=> ρ L/R = 2A₁
3R = ρ L/A₂
=> ρ L/R = 3A₂
6R = ρ L/A₃
=> ρ L/R = 6A₃
Equate ρ L/R
2A₁ = 3A₂ = 6A₃
Dividing by 6
=> A₁/3 = A₂/2 = A₃/1
=> A₁ : A₂ : A₃ = 3 : 2 : 1
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