Final answer:
To calculate the resistance of a gold wire, one must use the resistance formula R = ρL/A, converting all units to meters, inputting the resistivity of gold, and solving for R.
Step-by-step explanation:
To find the resistance of a 1.7-meter-long gold wire that is 0.70 mm in diameter, we need to use the formula for resistance, which is R = ρL/A, where R is resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
First, we convert the diameter to meters, which gives us 0.0007 meters. The cross-sectional area A is π(d/2)^2. Plugging in the diameter, we get:
A = π(0.0007/2)^2
The resistivity (ρ) for gold at 20 °C is approximately 2.44 x 10^-8 Ωm. Therefore, the resistance R using the given length of 1.7 meters can be calculated as follows:
R = (2.44 x 10^-8 Ωm)(1.7 m) / [π(0.00035 m)^2]
After we calculate the resistance with the formula, we can provide the specific value for the resistance of the gold wire.