A certain piece of copper is to be shaped into a conductor of minimum resistance, its length and cross sectional area should be

Options

A. L and A
B. 2L and `(A)/(2)`
C. `(L)/(2)` and 2A
D. 3L and `(A)/(3)`

Answer

To determine the length and cross-sectional area of a copper conductor that minimizes resistance, we can use the formula for resistance in a conductor:

\[ R = \frac{\rho L}{A} \]

where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material (copper in this case),
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The resistance \( R \) is directly proportional to the length \( L \) of the conductor and inversely proportional to the cross-sectional area \( A \). This means that to minimize resistance, we need to either decrease the length or increase the area.

2. **Minimize Length**:
If we want to minimize resistance, we should aim to keep the length \( L \) as small as possible. However, the length cannot be zero, as that would not constitute a conductor.

3. **Maximize Cross-Sectional Area**:
To further minimize the resistance, we should maximize the cross-sectional area \( A \). A larger area allows more current to flow through the conductor, thereby reducing resistance.

4. **Conclusion**:
Therefore, for a conductor made of copper to have minimum resistance, it should be designed with a **short length** and a **large cross-sectional area**.

### Final Answer:
- The length should be **minimum** (as short as practically possible).
- The cross-sectional area should be **maximum** (as large as practically possible).