What is the mass of a copper wire that will give a wire, 0.20mm in diameter, a resistance of 400 ohms
can you please show me the formulas
To find the mass of a copper wire that will give a wire with a certain diameter a specific resistance, we need to use a couple of formulas and some properties of copper.
First, we'll start with the formula to calculate the resistance of a wire:
Resistance (R) = (ρ * L) / A
Where:
R is the resistance of the wire,
ρ (rho) is the resistivity of the material (in this case, copper),
L is the length of the wire, and
A is the cross-sectional area of the wire.
Next, we need to find the formulas for resistivity (ρ) and cross-sectional area (A).
1) Resistivity:
The resistivity of copper at room temperature is approximately 1.68 × 10^-8 ohm-meter.
2) Cross-sectional area:
The cross-sectional area of a wire can be calculated using the formula:
A = π * r^2
Where:
A is the cross-sectional area,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r is the radius of the wire (half of the diameter).
Now, let's calculate the mass of the copper wire. To do this, we need to rearrange the resistance formula to solve for the mass:
Resistance (R) = (ρ * L) / A
Let's assume a length of wire (L) and rearrange the formula to solve for the mass (M):
M = (R * A) / ρ
Substituting the given values into the formula, we have:
M = (400 ohms * π * (0.20mm/2)^2) / (1.68 × 10^-8 ohm-meter)
Now, let's calculate the mass.
To calculate the mass, we need to convert the diameter from millimeters to meters:
0.20 mm = 0.20 × 0.001 m = 0.0002 m
Therefore,
M = (400 ohms * π * (0.0002m/2)^2) / (1.68 × 10^-8 ohm-meter)
Simplifying the equation,
M = (400 * 3.14159 * (0.0001)^2) / (1.68 × 10^-8)
Finally, evaluate the expression using a calculator to find the mass of the copper wire.