Final answer:
The wire's length can be calculated using Ohm’s Law and the resistance formula for a wire, involving the resistivity of copper, the potential difference applied, and the current flowing through the wire. The steps involve finding the resistance using Ohm's Law, calculating the cross-sectional area of the wire, and then solving for the wire's length.
Step-by-step explanation:
The question asks us to determine the length of a copper wire through which a current of 0.95 A is flowing when it is connected to a potential difference of 15 V. To find the length of the wire, we need to know the resistivity of copper and use Ohm’s Law along with the formula for the resistance of a wire.
Steps to Calculate the Length of the Wire:
- First, use Ohm’s Law to find the resistance: R = V / I, where V is the voltage (15 V) and I is the current (0.95 A).
- Next, use the resistance formula for a wire: R = ρL / A, where ρ is the resistivity of copper, L is the length of the wire we want to find, and A is the cross-sectional area of the wire, which is π(d/2)^2 with d being the diameter of the wire.
- Solve for L, taking into account that the resistivity of copper (ρ) is a known constant, and the diameter of the wire is given as 0.52 mm.
- To get the answer in kilometers, convert the length in meters to kilometers by dividing by 1000.
Using these steps, you will be able to calculate the length of the copper wire in kilometers. Remember, to apply these steps, we need the exact resistivity value for copper which is typically around 1.68×10-8 Ω·m at room temperature.