Resistivity of a conductor of length l and cross - section A is `rho` . If its length is doubled and area of cross-section is halved, then its new resistivity will be .

Options

A. `(rho)/(2)`
B. `4 rho`
C. `(rho)/(4)`
D. `rho`

Explanation

To solve the problem, we need to understand the concept of resistivity and how it relates to the dimensions of a conductor.

### Step-by-Step Solution:

1. **Understanding Resistivity**:
Resistivity (\(\rho\)) is a property of a material that quantifies how strongly it resists the flow of electric current. It is defined as:
\[ \rho = R \frac{A}{l} \]
where \(R\) is the resistance, \(A\) is the cross-sectional area, and \(l\) is the length of the conductor.

2. **Initial Conditions**:
- Let the initial length of the conductor be \(l\).
- Let the initial cross-sectional area be \(A\).
- The initial resistivity is given as \(\rho\).

3. **Changing Dimensions**:
- The length of the conductor is doubled: New length \(l' = 2l\).
- The area of cross-section is halved: New area \(A' = \frac{A}{2}\).

4. **Calculating New Resistivity**:
The resistivity of a material is a characteristic property that does not change with the dimensions of the conductor. Thus, even after changing the dimensions, the resistivity remains the same.

Therefore, the new resistivity \(\rho'\) is still:
\[ \rho' = \rho \]

5. **Conclusion**:
The new resistivity remains unchanged, so:
\[ \text{New Resistivity} = \rho \]

### Final Answer:
The new resistivity will be \(\rho\).

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