Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of 0.835. What is the resistance of the copper wire? Take the resistivity of copper to be 1.72 x 10-8 Ω·m, and that of aluminum to be 2.82 x 10-8 Ω·m.
The ratio of the resistances will be the same as the ratio of the resistivities, if lengths and diameters are the same.
R(Cu)/R(Al) = 1.72 x 10-8/2.82 x 10-8
= 0.61
R(Al) = 0.509 Ù
Well, for resistance of wire we have formula as,
R = (resistivity * length of wire ) / crosssectional area. As both wires are identical, there length and crossectional area are same. So, as resistance is directly praportional to resistivity,
R(Cu) / R(Al) = resistivity of copper / resistivity of Aluminum.
So, R(Cu) = R(Al ) * 1.7241* 10-8 / 2.82 x 10-8.
R(Cu) = 0.835 * 1.7241/ 2.82 = 0.51047518 ohm
Well, if you're looking for some electrical humor, I'll give it a shot!
Resistance is like the wire's way of saying, "Nope, no easy flow of current for you!" So, in this case, we have two wires - one aluminum and one copper - and we want to find the resistance of the copper wire.
The resistance of a wire can be calculated using the formula: R = ρ * L / A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.
Since the wires are identical (except for their material), we can assume that they have the same length and cross-sectional area. So, we just need to compare the resistivity of aluminum and copper to figure out the resistance of the copper wire.
Given ρ(copper) = 1.72 x 10^-8 Ω·m and ρ(aluminum) = 2.82 x 10^-8 Ω·m, it's clear that copper has lower resistivity.
So, if the aluminum wire has a resistance of 0.835, the copper wire will have a lower resistance. Remember, lower resistance means better flow of current!
But, to give you a more specific answer, I'll need the length and cross-sectional area of the wires. Without those, I'll just have to leave you momentarily "resisting" the complete answer.
To find the resistance of the copper wire, we can use the formula for resistance:
Resistance = (Resistivity x Length) / Area
Since the wires are identical in all aspects except the material, we can assume the length and cross-sectional area of both wires are the same.
Let's denote "R_Al" as the resistance of the aluminum wire, "R_Cu" as the resistance of the copper wire, "ρ_Al" as the resistivity of aluminum, and "ρ_Cu" as the resistivity of copper.
Given that R_Al = 0.835 Ω and ρ_Cu = 1.72 x 10^(-8) Ω·m, we need to find R_Cu.
We can rewrite the resistance formula as:
R = (ρ x L) / A
Since L and A are the same for both wires, we can write:
R_Al / R_Cu = (ρ_Al / ρ_Cu)
Therefore, we can rearrange the equation to solve for R_Cu:
R_Cu = R_Al x (ρ_Cu / ρ_Al)
Substituting the given values:
R_Cu = 0.835 Ω x (1.72 x 10^(-8) Ω·m / 2.82 x 10^(-8) Ω·m)
Simplifying the expression:
R_Cu = 0.835 Ω x 0.6106
R_Cu ≈ 0.509 Ω
Therefore, the resistance of the copper wire is approximately 0.509 Ω.
To find the resistance of the copper wire, we can use the formula for resistance:
Resistance (R) = Resistivity (ρ) * Length (L) / Area (A)
Given that the wires are identical except for the material (aluminum and copper) and the resistance of the aluminum wire (R_aluminum = 0.835), we can equate the resistance of the aluminum wire to the resistance formula and solve for the resistance of the copper wire.
Let's assume the length and area of the wires are the same, so we can cancel them out. Therefore, the resistances are directly proportional to the resistivity:
R_aluminum / R_copper = ρ_aluminum / ρ_copper
Substituting the given values of resistivities:
0.835 / R_copper = (2.82 x 10^(-8) Ω·m) / (1.72 x 10^(-8) Ω·m)
Simplifying the expression:
0.835 / R_copper = 1.6395
Now, we can solve for R_copper by rearranging the equation:
R_copper = 0.835 / 1.6395
R_copper ≈ 0.509 Ω
Therefore, the resistance of the copper wire is approximately 0.509 Ω.