one gram of gold can be drawn into a wire 2.25 km long. What is the resistance of such a wire at 20°C?
To find the resistance of a wire, we need to know its resistivity, which is the inherent property of a material to resist the flow of electric current. Resistivity is usually given in units of ohm-meter (Ω⋅m).
In this case, we are provided with the length and mass of the wire, but we need additional information to calculate the resistivity first. Once we have the resistivity, we can then use the length and cross-sectional area of the wire to calculate the resistance.
To proceed, we need to know the resistivity of gold at 20°C. The resistivity of gold varies with temperature, but for simplicity, let's assume it remains constant at room temperature (20°C). The resistivity of gold at room temperature is approximately 2.44 × 10^(-8) Ω⋅m.
Now that we have the resistivity, we can proceed with the calculation:
1. Convert the length of the wire from kilometers to meters:
2.25 km = 2.25 × 1000 = 2250 meters
2. Calculate the cross-sectional area of the wire. Since we are not given any information about the shape of the wire, we cannot directly determine the area. Assuming the wire is a perfect cylinder, we need to know either the diameter or radius. Without this information, we cannot proceed further with the calculations.
Therefore, the resistance of the wire at 20°C cannot be determined without knowing the cross-sectional area (diameter or radius) of the wire.