Final answer:
To find the resistance of a cylindrical wire, we can use the formula R = (ρ * L) / (A), where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. In this case, the wire is made of gold, so we need to use the resistivity value of gold and calculate the cross-sectional area using the given diameter. Once we have the cross-sectional area, we can plug in the values and calculate the resistance of the gold wire.
Step-by-step explanation:
To calculate the resistance of a cylindrical wire, we need to use the formula:
R = (ρ * L) / (A)
Where:
- R is the resistance of the wire
- ρ (rho) is the resistivity of the material
- L is the length of the wire
- A is the cross-sectional area of the wire
In this case, the wire is made of gold. The resistivity of gold is ρ = 2.44 × 10^-8 Ω.m.
The length of the wire is L = 0.5 m.
The diameter of the wire is given as 0.75 cm, so we need to calculate the cross-sectional area using the formula:
A = π * (d/2)^2
Where:
- d is the diameter of the wire
Once we have the cross-sectional area, we can substitute the values into the resistance formula to find the resistance of the gold wire.
Remember to convert the diameter to meters before calculating the cross-sectional area.