A 15 ohm resistor is made from a copper wire of mass 14.2 grams. What is the wire's diameter and length?

resistance=resisitiveity*length/area

mass=density*length*area
area=mass/density*length

resistance=resistivity*length/(mass/density8lengty)

resistance=resititivey*length^2*density/mass

solve for length, then go back and solve for area. Yes, you have to look up resisitivey and density of copper.

To find the wire's diameter and length, we need to make some assumptions and use formulas involving the resistivity of copper.

Assuming the wire is cylindrical in shape, we can use the formula for resistance:

Resistance (R) = (Resistivity (ρ) * Length (L)) / Cross-sectional Area (A)

Given that the resistance is 15 ohms, we can substitute this value into the formula:

15 = (ρ * L) / A

Rearranging the formula, we get:

A = (ρ * L) / 15

Now, let's move on to finding the cross-sectional area (A) of the wire.

The resistivity of copper is typically about 1.7 x 10^-8 Ωm.

We know that the mass of the wire is 14.2 grams, but we need to convert it to kilograms for the formula. So, mass (m) = 0.0142 kg.

The density of copper is approximately 8.96 grams per cubic centimeter (g/cm^3).

Since the wire is cylindrical, we can use the formula for the volume of a cylinder:

Volume (V) = π * (diameter (d)/2)^2 * Length (L)

The density formula states that density (ρ) = mass (m) / volume (V).

So, using the volume formula, we can rearrange it to get V = m / ρ.

Substituting the values, we can calculate the volume of the wire:

V = 0.0142 kg / (8.96 g/cm^3)

Now, we can express the volume in terms of meters cubed:

V = (0.0142 kg / 1000 g) / (8.96 g/cm^3 * 1000000 cm^3/m^3)

Next, we equate this volume with the volume formula for a cylinder:

V = π * (d/2)^2 * L

Substituting the earlier expression for V, we have:

(0.0142 kg / 1000 g) / (8.96 g/cm^3 * 1000000 cm^3/m^3) = π * (d/2)^2 * L

Now, we have two equations:

15 = (ρ * L) / A
(0.0142 kg / 1000 g) / (8.96 g/cm^3 * 1000000 cm^3/m^3) = π * (d/2)^2 * L

Using these equations, we can solve for the wire's diameter (d) and length (L). However, due to the complexity of the calculations involved, it would be more efficient to use specialized software or an appropriate online calculator that can handle these calculations for you.