A gold wire has a cross-sectional area of 1.0 cm^2 and a resistivity of 2.8 × 10^-8 Ω ∙ m at 20°C. How long would it have to be to have a resistance of 0.001 Ω?

Respuesta :

Answer:

Length, l = 3.57 meters

Explanation:

It is given that,

Area of cross-section of gold wire, [tex]A=1\ cm^2=0.0001\ m^2[/tex]

Resistivity of gold wire, [tex]\rho=2.8\times 10^{-8}\ \Omega-m[/tex]

Resistance, R = 0.001 ohms

Resistance in terms of length and area is given by :

[tex]R=\rho \dfrac{l}{A}[/tex]

[tex]l=\dfrac{RA}{\rho}[/tex]

[tex]l=\dfrac{0.001\times 0.0001}{2.8\times 10^{-8}}[/tex]

l = 3.57 meters

So, the length of the wire is 3.57 meters. Hence, this is the required solution.