Question

Three resistances 2R, 3R and 6R of same material and same length having area of cross-section in ratio ​

Answer 1

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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