If 750 m of 3.00-mm-diameter wire has a resistance of 27.6, what length of similar wire 5.00 mm in diameter will have the same resistance?
To solve this problem, we can use the formula for resistance:
Resistance = (resistivity * length) / area
First, let's find the area of the first wire:
Area = π * (radius^2)
= π * ((diameter / 2)^2)
= π * ((3.00 mm / 2)^2)
Next, let's calculate the resistivity of the wire. The resistivity depends on the material the wire is made of. For simplicity, let's assume it is copper, which has a resistivity of 1.72 x 10^-8 Ω*m.
Now we can rearrange the resistance formula to solve for the length:
Length = (Resistance * Area) / resistivity
Let's substitute the given values into the formulas:
Area = π * ((3.00 mm / 2)^2)
Resistivity = 1.72 x 10^-8 Ω*m
Resistance = 27.6 Ω
Length = (27.6 Ω * Area) / (1.72 x 10^-8 Ω*m)
Now, we need to find the area of the new wire:
Area (new wire) = π * ((diameter / 2)^2)
= π * ((5.00 mm / 2)^2)
Finally, we can substitute the given values into the formula to find the length of the similar wire:
Length (new wire) = (27.6 Ω * Area (new wire)) / (1.72 x 10^-8 Ω*m)
By calculating the values, you will be able to find the length of the wire with a diameter of 5.00 mm that will have the same resistance as the original wire.