The resistivity of gold is at a temperature of 20°C. A gold wire, 1.8 mm in diameter and 14 cm long, carries a current of 480 ma. The power dissipated in the wire is closest to:
0.25mW
To calculate the power dissipated in the wire, we need to use the formula:
P = I^2 * R
where P is power, I is current, and R is resistance. To find the resistance, we can use the formula:
R = (ρ * L) / A
where ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire.
First, let's calculate the resistance:
R = (ρ * L) / A
The given length is 14 cm, which is 0.14 m.
The diameter of the wire is 1.8 mm, which is 0.0018 m. Therefore, the radius is 0.0009 m.
The cross-sectional area can be calculated using the formula:
A = π * r^2
A = π * (0.0009)^2
≈ 0.0025437 m^2
Now we can substitute the values into the resistance formula:
R = (ρ * L) / A
= (2.44 * 10^-8 * 0.14) / 0.0025437
≈ 1.3441 * 10^-6 Ω
Now, let's calculate the power dissipated:
P = I^2 * R
= (0.48)^2 * 1.3441 * 10^-6
≈ 1.2349 * 10^-4 W
Therefore, the power dissipated in the wire is closest to 0.000123 W (rounded to 6 significant figures).
To find the power dissipated in the gold wire, we need to use the formula for power, which is given by:
P = I^2 * R
where P is the power, I is the current, and R is the resistance.
First, let's calculate the resistance of the gold wire. The formula for resistance is given by:
R = (ρ * L) / A
where R is the resistance, ρ (rho) is the resistivity of gold, L is the length of the wire, and A is the cross-sectional area of the wire.
To find the cross-sectional area of the wire, we need to use the formula for the area of a circle:
A = π * r^2
where r is the radius of the wire.
Given that the diameter of the wire is 1.8 mm, we can find the radius by dividing the diameter by 2:
r = 1.8 mm / 2 = 0.9 mm = 0.009 m
Now, we can calculate the cross-sectional area:
A = π * (0.009 m)^2 = π * 0.000081 m^2
Next, we need to calculate the resistance:
R = (ρ * L) / A
Given that the length of the wire is 14 cm = 0.14 m, and the resistivity of gold is 2.44 x 10^-8 ohm·m (at 20°C), we can substitute these values into the formula:
R = (2.44 x 10^-8 ohm·m * 0.14 m) / (π * 0.000081 m^2)
Now we have the resistance of the wire.
To find the power, we substitute the values into the power formula:
P = (0.48 A)^2 * R
where the current is 480 mA = 0.48 A.
Substituting the values for the resistance and current, we can calculate the power:
P = (0.48 A)^2 * R
Finally, calculate the value of P to get the answer.
(Note: The value of the resistivity of gold at 20°C, and the final calculations to find the power have not been provided in the question, so the final answer cannot be determined without this information.)