A copper wire and a constantin wire of the same length have the same potential difference. Determine the ratio of radii needed to ensure the current that flows through each wire is the same.
Resistivity of copper = 1.67 x 10^-8 ohms per metre
Resistivity of constantin = 4.9 x 10^-7 ohms per metre
The answer is copper:constantin = 5.4:1 (54:10)
So i just wanna know the steps to arrive to this answer, it would be greatly appreciated!
Resistivity of copper = 1.67 x 10^-8 ohms per metre
Resistivity of constantin = 4.9 x 10^-7 ohms per metre
The answer is copper:constantin = 5.4:1 (54:10)
So i just wanna know the steps to arrive to this answer, it would be greatly appreciated!
-
as per question V(copper) = V(constantan) ie., i R(copper) = i R(constantan)
or rho(copper) L/ pi r1^2 = rho(constantan) L / pi r2^2
ie., r1^2 / r2^2 = rho(copper) / rho(constantan) = 1.67 x10^-8 / 4.9 x10^-7 = 1.67 / 49
ie., r1 / r2 = 0.1846 or r2 / r1 = 5.41
hence radius of copper : radius of constantan = 5.41 : 1
or rho(copper) L/ pi r1^2 = rho(constantan) L / pi r2^2
ie., r1^2 / r2^2 = rho(copper) / rho(constantan) = 1.67 x10^-8 / 4.9 x10^-7 = 1.67 / 49
ie., r1 / r2 = 0.1846 or r2 / r1 = 5.41
hence radius of copper : radius of constantan = 5.41 : 1