Question

Two wires have lenghts,resisitance,resistivity each in the ratio 1:2 what is the radius of their diameters

Answer 1

Answer:1:2 R= rho l / a

Answer 2

Considering  length as L₁, resistance as R₁ and resistivity as ρ₁ for wire 1 and length as L₂, resistance as R₂ and resistivity as ρ₂ for wire 2.

Now we know resistivity is expressed as,

ρ = (RA)/l = {R π(d/2)²}/ l

(4ρ l/ 2π) = d²------(A)

Also given ratio of the mentioned parameters for both the wires is 1:2 ----(B)

Reducing equation A we get with appropriate parameters e get,

(4ρ₁ l₁/ 2π)/(4ρ₂ l₂/ 2π) = d₁²/d₂²

According to statement (B)

1/2 = d₁²/d₂²

d₁/d₂ = 1/√2