Respuesta :
(a) The resistivity of a substance is the resistance of a substance per unit length and per unit cross section at a given temperature. Since both wires are made of the same substance and I assume are at the same temperature, the ratio i2/i1 for those wires will be 1.
(b) The resistance of a wire is described by the following equation
R = pl/A
where
R = Resistance
p = resistivity of material
l = length
A = cross sectional area
Now the cross section of the wire is defined as pi*r^2 and r is one half of the diameter. So wire 2 will have a radius twice that of wire 1, so the cross section will differ by the square of the differences in the radius. So wire 2 will have a cross section 2^2 = 4 times that of wire 1. So the ratio
r2/r1 = (p*2/4)/(p*1/1) = (2/4)(1/1) = 0.5/1 = 0.5
So wire 2 will have half the resistance of wire 1.
The ratios of the resistivities and the resistances of the two wires will be 1 and 2.
What is resistance?
Resistance is a type of opposition force due to which the flow of current is reduced in the material or wire. Resistance is the enemy of the flow of current.
The given data in the problem is;
Wires 1 and 2 are made of the same metal [tex](\rho_1=\rho_2)[/tex]
[tex]\rm L_2=2L_1 \\\\\ D_2=2D_1[/tex]
The material of the material is the same then the ratio of the resistivity will be found as;
[tex]\rm \frac{\rho_2}{\rho_1} =1[/tex]
The ratio of the resistance is found by;
[tex]\rm \frac{R_2}{R_1} = \frac{\rho_1}{L_1A_1} \times \frac{L_2A_2}{\rho_2} \\\\ \rm \frac{R_2}{R_1} =\frac{L_2}{d_1^2} \times \frac{d_2^2}{L_2} \\\\\ \rm \frac{R_2}{R_1} =\frac{2L_1}{4d_1^2} \times \frac{d_2^2}{L_1} \\\\ R_2 = 2R_1[/tex]
Hence the ratios of the resistivities and the resistances of the two wires will be 1 and 2.
To learn more about the resistance refer to the link;
https://brainly.com/question/20708652
