You've made the finals of the Science Olympics! As one of your tasks, you're given 1.8g of copper and asked to make a wire, using all the metal, with a resistance of 1.3 Ohm. Copper has a density of 8900 kg/m^3.
What length will you choose for your wire(in meters)?
What diameter will you choose for your wire(in millimeters)?
writeacher is a prude
To quote one of our very good math and science tutors: “You will find here at Jiskha that long series of questions, posted with no evidence of effort or thought by the person posting, will not be answered. We will gladly respond to your future questions in which your thoughts are included.”
Writeacher is an amazing teacher! Thank you so much for your help. I'm currently paying hundreds of dollars at a top 10 university where they don't teach you anything at all. So coming here to find the master himself, writeacher, give me advice on how to start a problem was incredibly lucky. Thank you for providing me with the motivation I needed to go ahead and start my homework without any knowledge of how to do it!
To determine the length and diameter of the wire required, we need to use the formula for the resistance of a wire:
Resistance (R) = (resistivity * length) / cross-sectional area
Given that the resistance is 1.3 Ohm and the copper wire has a resistivity of 1.68 x 10^(-8) Ohm·m, we can rearrange the formula to solve for length and cross-sectional area.
To find the length (L) of the wire:
1. Rearrange the formula to solve for length:
Length (L) = (Resistance * cross-sectional area) / resistivity
2. Calculate the cross-sectional area:
The mass (m) of the copper wire is given as 1.8g = 0.0018kg.
The density (ρ) of copper is 8900 kg/m^3.
The volume (V) of the wire can be calculated using the formula:
Volume (V) = mass / density
So, V = 0.0018kg / 8900 kg/m^3.
The cross-sectional area (A) can then be calculated using the formula:
Area (A) = V/L
Substituting the values we have:
A = (0.0018kg / 8900 kg/m^3) / L
3. Substitute the values into the length formula:
L = (Resistance * A) / resistivity
Substituting the resistance value of 1.3 Ohm, resistivity value of 1.68 x 10^(-8) Ohm·m, and the calculated value of A from step 2 will give us the length (L) of the wire.
To find the diameter (d) of the wire:
1. Use the formula for the cross-sectional area of a circle:
Area (A) = π * (d/2)^2
2. Rearrange the formula to solve for diameter:
d = √((4 * A) / π)
3. Substitute the calculated value of A from step 2 into the diameter formula.
Using these formulas, you can calculate the length and diameter of the wire.