A wire of cross-sectional area 5.00x10^-6 m^2 has a resistance of 1.75 ohm. what is the resistance of a wire of the same material and length as the first wire, but with a cross-sectional area of 8.75x10^-6 m^2?

I really want to understand what to do here, so detailed steps will be greatly appreciated.

To find the resistance of the second wire, we can use the formula for resistance:

R = ρ * (L / A)

Where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Since we are comparing two wires of the same material and length, the resistivity and length will remain the same for both wires.

To find the resistance of the first wire, we are given its cross-sectional area (A1 = 5.00x10^-6 m^2) and resistance (R1 = 1.75 ohm).

Let's substitute the given values into our formula for the first wire:

1.75 = ρ * (L / 5.00x10^-6)

Now, we can isolate ρ in terms of R1 and A1:

ρ = (R1 * A1) / L

Now that we have the value of resistivity ρ, we can find the resistance of the second wire using its cross-sectional area (A2 = 8.75x10^-6 m^2):

R2 = ρ * (L / A2)

Substituting the value of ρ into the formula:

R2 = [(R1 * A1) / L] * (L / A2)

Simplifying the equation:

R2 = (R1 * A1) / A2

Now we can substitute the values given for R1, A1, and A2 into the equation to find the resistance of the second wire:

R2 = (1.75 * 5.00x10^-6) / 8.75x10^-6

R2 = 0.875 ohm

Therefore, the resistance of the wire with a cross-sectional area of 8.75x10^-6 m^2 is 0.875 ohm.