Respuesta :
Answer:
Ra / Rb = 3
Explanation:
The resistance is defined by the expression
r = ρ L / A
where A is the area of the wire and L is the length
let's find the area of each wire
a) solid wire (A) of d₁ = 1 m
r = d₁ / 2 = 0.5 m
A = π r²
A = π 0.5²
R_a = [tex]\frac{\rho \ L}{\pi \ 0.5^2}[/tex]
R_a = 4 \frac{\rho \ L}{\pi }
b) hollow tube (B) of d₁ = 1 m and d₂ = 2m
the radios are
r₁ = 0.5 m
r₂ = 1 m
the area is
A = π r₂² - π r₁²
A = π (r₂² - r₁²)
A = π (1² - 0.5²)
A = π 0.75
resistance is
R_b = [tex]\frac{ \rho \ L }{\pi \ 0.75}[/tex]
R_b = 1.33 \frac{ \rho \ L }{\pi }
therefore the relationship between these two resistances is
Ra / Rb = 4 / 1.33
Ra / Rb = 3
