Respuesta :
Answer:
Therefore,
The resistance ratio RA/RB, measured between their ends is
[tex]\dfrac{R_{A}}{R_{B}}=\dfrac{1}{4}=0.25[/tex]
Explanation:
Given:
Consider Two conductors are made of the same material (A & B)and have the same length.,
[tex]L_{A}=L_{B}[/tex]
Diameters,
[tex]d_{A}=2\ mm[/tex]
[tex]d_{B}=2\ mm....outer\\d_{B}=1\ mm.....inner[/tex]
Radius is half of Diameter,
Therefore
[tex]r_{A}= \dfrac{2}{2}=1\ mm\\\\r_{B}=\dfrac{2-1}{2}...hollow\ tube\\r_{B}=0.5\ mm[/tex]
To Find:
[tex]\dfrac{R_{A}}{R_{B}}=?[/tex] (resistance ratio)
Solution:
Resistance for long wire with a Area of cross section is given by
[tex]R=\dfrac{\rho\times l}{A}[/tex]
Where,
R = Resistance
l= length
A = Area of cross section = πr²
[tex]\rho=Resistivity\ of\ material[/tex]
i.e
When
material and length is same then Resistance is inversely proportional to Area,
[tex]R\alpha \dfrac{1}{A}[/tex]
Hence,
[tex]R_{A}\alpha \dfrac{1}{A_{A}}[/tex]
And
[tex]R_{B}\alpha \dfrac{1}{A_{B}}[/tex]
Equating we get
[tex]\dfrac{R_{A}}{R_{B}}=\dfrac{A_{B}}{A_{A}}=\dfrac{\pi r_{B}^{2}}{\pi r_{A}^{2}}[/tex]
Substituting the values we get
[tex]\dfrac{R_{A}}{R_{B}}=\dfrac{0.5^{2}}{1^{2}}=0.25=\dfrac{1}{4}[/tex]
Therefore,
The resistance ratio RA/RB, measured between their ends is
[tex]\dfrac{R_{A}}{R_{B}}=\dfrac{1}{4}=0.25[/tex]
