To find the resistance $R$ of the copper conductor, we use the following formula:

$R = \rho \cdot \frac{L}{A}$

Where:

• $R$ is the resistance in ohms (Ω),
• $\rho$ is the resistivity of the material (copper) in ohm-centimeter (Ω·cm),
• $L$ is the length of the conductor in centimeters (cm),
• $A$ is the cross-sectional area in square centimeters (cm²).

Step 1: Convert the given values into appropriate units

• The length $L$ is given as 200 meters, which we convert to centimeters:
  $L = 200 \, \text{m} = 200 \times 100 = 20,000 \, \text{cm}$,
• The cross-sectional area $A$ is already given in square centimeters: $A = 0.26 \, \text{cm}^2$,
• The resistivity of copper at 20℃ is given as $\rho = 0.00000172 \, \Omega \cdot \text{cm}$.

Step 2: Calculate the resistance

Now, substitute the values into the resistance formula:

$R = 0.00000172 \, \Omega \cdot \text{cm} \times \frac{20,000 \, \text{cm}}{0.26 \, \text{cm}^2}$

Let's compute that.The resistance of the copper conductor at 20°C is approximately $0.132 \, \Omega$.

Do you need further details or have any questions?

Here are 5 related questions for deeper understanding:

1. How does temperature affect the resistance of a copper conductor?
2. What would the resistance be if the length of the conductor were doubled?
3. How would a different material, like aluminum, affect the resistance calculation?
4. What is the relationship between cross-sectional area and resistance?
5. How does resistivity vary with temperature for metals like copper?

Tip: For long wires, even a small increase in temperature can significantly raise the resistance, as most metals have positive temperature coefficients.