What is the resistance, at 20℃, of an electric motor winding that uses 200m of copper
conductor which is 0.26-centimeter square (𝑐𝑚2 ) (approximately 3/16 in. by 3/16 in.) The 
resistivity of copper at 20℃ is 0.00000172Ω.cm.

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.

What is the resistance, at 20℃, of an electric motor winding that uses 200m of copper conductor which is 0.26-centimeter square (𝑐𝑚²) (approximately 3/16 in. by 3/16 in.)? The resistivity of copper at 20℃ is 0.00000172Ω·cm.

Learn how to calculate the resistance of a 200-meter long copper conductor with a cross-sectional area of 0.26 cm² at 20°C. Using the resistivity of copper (0.00000172 Ω·cm), this step-by-step solution demonstrates the formula R = ρ * (L / A) for determining resistance. Ideal for high school students studying physics.

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