The length and radii of three wires of the same metal are in the ratio of 2:3:4 and 3:4:5 . . .

Question : The length and radii of three wires of the same metal are in the ratio of 2:3:4 and 3:4:5 respectively. They are joined in parallel and included in a circuit having 5 Ampere current. Find the current in each wire. 

Doubt by Suhani

Solution : 

L₁:L₂:L₃=2:3:4
r₁:r₂:r₃=3:4:5
We know, 
Area of cross section of wires 
A=πr²
A∝r²
So 
A₁:A₂:A₃=9:16:25
Also 
R=ρL/A
R∝L/A
R₁:R₂:R₃=2/9:3/16:4/25

We know, 
V=IR
I=V/R
Since the wires are connected in series so the potential across each of them remains same. 
Hence, 
I∝1/R
I₁:I₂:I₃=9/2:16/3:25/4

I₁:I₂:I₃=54:64:75

Also I₁+I₂+I₃ = 5 A

I₁=[54/(54+64+75)]×5
I₁=[54/193]×5
I₁=1.39
I₁=1.4 A

I₂=[64/(54+64+75)]×5
I₂=[64/193]×5
I₂=1.658
I₂=1.66 A

I₃=[75/(54+64+75)]×5
I₃=[75/193]×5
I₃=1.943 A
I₃=1.94 A