Answer:
RA / RB = 8.33
Explanation:
The resistance in terms of area is given by the following equation:
R = d * L / A
the density being the same in both cases, L the length, which is the same in both conductors and A the area that it does vary.
Now, in the case of conductor A, the area would be:
AA = pi * rA ^ 2
we know that d / 2 = r, therefore:
AA = (pi / 4) * dA ^ 2
Replacing in the resistance formula:
RA = 4 * dA * L / (pi * d ^ 2)
In the case of B we have that the area we want to know is equal to the area on the outside minus the area on the inside
AB = pi * rBo ^ 2 - pi * rBi ^ 2
expressing in diameters:
AB = (pi / 4) * (dBo ^ 2 - dBi ^ 2)
Replacing in R
RB = 4 * d * L / (pi * (dBo ^ 2 - dBi ^ 2))
To know RA / RB we divide these two expressions, the term 4 * d * L is canceled, which is the same in both cases and we are left with:
RA / RB = (dBo ^ 2 - dBi ^ 2) / dA ^ 2
Replacing these values:
RA / RB = (8 ^ 2 - 4 ^ 2) /2.4^2
RA / RB = 8.33
Answer:
[tex]\frac{R_{A} }{R_{B} }[/tex] = [tex]\frac{25}{3}[/tex]
Explanation:
For the two conductors A and B, the required general formula is;
R = ρl ÷ A
But since the two conductors are made of the same material,
ρA = ρB
Also, they have the same length,
lA = lB
So that,
[tex]\frac{R_{A} }{R_{B} }[/tex] = [tex]\frac{A_{B} }{A_{A} }[/tex]
Area can be calculated by [tex]\pi r^{2}[/tex].
Conductor A has diameter 2.4mm, thus its radius is 1.2mm. Conductor B has outside diameter 8.0mm of radius 4.0 and inside diameter 4.0mm of radius 2.0mm. Thus,
[tex]\frac{R_{A} }{R_{B} }[/tex] = [tex]\frac{\pi*(16 - 4)*10^{-6}}{\pi*1.44*10^{-6} }[/tex]
By appropriate divisions,
[tex]\frac{R_{A} }{R_{B} }[/tex] = [tex]\frac{12}{1.44}[/tex]
= [tex]\frac{1200}{144}[/tex]
[tex]\frac{R_{A} }{R_{B} }[/tex] = [tex]\frac{25}{3}[/tex]
The resistance ratio measured between their ends is [tex]\frac{25}{3}[/tex].
