Respuesta :
Answer:
(I). The resistance of the copper wire is 0.0742 Ω.
(II). The resistance of the carbon piece is 1.75 Ω.
Explanation:
Given that,
Length of copper wire = 1.70 m
Diameter = 0.700 mm
Length of carbon piece = 20.0 cm
Cross section area[tex]A = (2.00\times10^{-3})^2\ m[/tex]
(I). We need to calculate the area of copper wire
Using formula of area
[tex]A=\pi r^2[/tex]
[tex]A=3.14\times(\dfrac{0.700\times10^{-3}}{2})^2[/tex]
We need to calculate the resistance
Using formula of resistance
[tex]R=\dfrac{\rho l}{A}[/tex]
Put the value into the formula
[tex]R=\dfrac{1.68\times10^{-8}\times1.70}{3.14\times(\dfrac{0.700\times10^{-3}}{2})^2}[/tex]
[tex]R=0.0742\ \Omega[/tex]
(II). We need to calculate the resistance
Using formula of resistance
[tex]R=\dfrac{\rho l}{A}[/tex]
Put the value into the formula
[tex]R=\dfrac{3.5\times10^{-5}\times20\times10^{-2}}{(2.00\times10^{-3})^2}[/tex]
[tex]R=1.75\ \Omega[/tex]
Hence, (I). The resistance of the copper wire is 0.0742 Ω.
(II). The resistance of the carbon piece is 1.75 Ω.
The resistance of the long copper wire is 0.0742 ohms and the resistance of long carbon piece is 1.75 ohms.
What is the resistance?
Resistance is obstacle for the current flow in the circuit. It is the measure of reverse act to current flow in through a material.
It can be given as,
[tex]R=\dfrac{\rho \times l}{A}[/tex]
Here, [tex]\rho[/tex] is the specific resistance (l) is the length of the material and (A) is the cross sectional area of the material.
For part A of the problem, the length of the wire is 1.70 meters and the diameter of the wire is 0.700 meters. Thus the cross sectional area of the wire is,
[tex]A=\pi (0.7\times10^{-3})^2\\A=1.54\times10^{-6}\rm m^2[/tex]
As the specific resistance of the copper wire is [tex]1.68\times10^{-8}[/tex] ohm-meter. Thus the resistance of the copper wire is,
[tex]R=\dfrac{1.68\times10^{-8}\times1.70 }{1.54\times10^{-6}}\\R=0.0742\rm ohm[/tex]
For part B of the problem, the length of the carbon piece is 20 cm and the cross section dimensions of the carbon piece is 2.00 mm x 2.00. Thus the cross sectional area of the wire is,
[tex]A=4\times10^{-6}\rm m^2[/tex]
As the specific resistance of the carbon piece is [tex]1.68\times10^{-8}[/tex] ohm-meter. Thus the resistance of the carbon piece is,
[tex]R=\dfrac{3.15\times10^{-5}\times20\times10^{-2} }{4\times10^{-6}}\\R=1.75\rm ohm[/tex]
Thus, the resistance of the long copper wire is 0.0742 ohms and the resistance of long carbon piece is 1.75 ohms.
Learn more about the resistance here;
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