What is the resistance of a 4.00 m length of copper wire having a diameter of 2.00 mm at a temperature of 20 degrees?
R= ?
L= 4.00 m
resistivity= 1.72 * 10^-8 ohm-meters
A= ?
A= pi*r^2
change 2 mm to .002m, square it and multiply by 3.14
I got .00001256
Is this right so far?
Yes, you are correct so far. You have successfully converted the diameter to the radius and then used the formula for the area of a circle to find the cross-sectional area of the wire.
Now, you just need to use the formula for resistance (R = resistivity * L / A) to find the resistance of the wire.
R = (1.72 * 10^-8 ohm-meters) * (4.00 m) / (0.00001256 m^2)
R = 5.47 ohms (approximately, after rounding)
So, the resistance of the wire is approximately 5.47 ohms at 20 degrees Celsius.
Yes, you're correct so far. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter is given as 2.00 mm, so the radius would be half of that, which is 1.00 mm or 0.001 m. Squaring the radius and multiplying by π, you correctly calculated the area to be approximately 0.00001256 square meters. Well done!
Yes, you are on the right track!
To find the resistance (R) of a wire, you need to know the resistivity of the material (ρ), the length of the wire (L), and the cross-sectional area of the wire (A).
To calculate the cross-sectional area (A) of the wire, you correctly used the formula A = π * r^2, where r is the radius of the wire. By converting the diameter of 2.00 mm to a radius of 0.001 m (2.00 mm = 0.002 m), squaring it (0.001 m * 0.001 m = 0.000001 m^2), and multiplying by π (0.000001 m^2 * π ≈ 0.00000314 m^2), you correctly obtained a value of approximately 0.00000314 m^2. However, you made a slight error in rounding off the value of π. The correct value of A would be approximately 0.00000314 m^2 or 3.14 x 10^-6 m^2.
Next, you need to use the resistivity of copper (1.72 * 10^-8 ohm-meters) along with the length of the wire (4.00 m) and the calculated cross-sectional area (A = 3.14 x 10^-6 m^2) to find the resistance (R).
The formula to calculate the resistance of a wire is R = ρ * (L / A). Plugging in the values, we get R ≈ (1.72 * 10^-8 ohm-meters) * (4.00 m / 3.14 x 10^-6 m^2).
Simplifying this expression, R ≈ 5.48 ohms.
Therefore, the resistance of the 4.00 m length of copper wire, with a diameter of 2.00 mm, at a temperature of 20 degrees, is approximately 5.48 ohms.