The same mass of aluminium is drawn into two wires 1 mm and 2 mm thick two wires are connected in series and current is passed through them heat produced in the wire is in ratio
Answers
Answer:
16 : 1 Ratio ( in circular)
4 : 1 in rectangular
Explanation:
The same mass of aluminium is drawn into two wires 1 mm and 2 mm thick two wires are connected in series and current is passed through them heat produced in the wire is in ratio
The same mass of aluminium is drawn
=> Volume would be Same = V
V = Area & Length
Let say thickness means here = Diameter
Radius = Diameter/2
Area = A₁ = π (1/2)² = π/4
=> L₁ = V/A₁ = V/(π/4) = 4V/ π
R₁ = ρL₁/A₁ = ρ(4V/ π)/(π/4) = ρ16V/π²
Area = A₂ = π (2/2)² = π
=> L₂ = V/A₂ = V/π
R₂ = ρL₂/A₂ = ρ(V/π)/π = ρV/π²
R₁ = 16R₂
Heat Produced = I²R₁ & I²R₂
=> I²16R₂ & I²R₂
=> 16 : 1 Ratio
V = Area & Length
Let say thickness means here = Thickness
& Width is same in both
Area = A₁ = 1 * W
=> L₁ = V/W
R₁ = ρL₁/A₁ = ρ(V/ W)/(W) = ρV/W²
Area = A₂ = 2 * W = 2W
=> L₂ = V/A₂ = V/2W
R₂ = ρL₂/A₂ = ρ(V/2W)/2W = ρV/4W²
R₁ = 4R₂
Heat Produced = I²R₁ & I²R₂
=> I²4R₂ & I²R₂
=> 4 : 1 Ratio