Conductivity of a conductor of length L and radius of cross-section r at temperature `t^(@) C ` is `sigma ` . If its length is doubled and radius is halved at same temperature, then new conductivity of the conductor will be

Options

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

Answer

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

### Step-by-step Solution:

1. **Understanding Conductivity**:
Conductivity (σ) is a property of the material that indicates how well it can conduct electricity. It is defined as the reciprocal of resistivity (ρ) and is independent of the dimensions of the conductor.

2. **Initial Conditions**:
- Length of the conductor (L) = L
- Radius of the conductor (r) = r
- Cross-sectional area (A) = πr²
- Conductivity (σ) = σ

3. **New Conditions**:
- New length of the conductor = 2L (length is doubled)
- New radius of the conductor = r/2 (radius is halved)
- New cross-sectional area (A') = π(r/2)² = π(r²/4) = πr²/4

4. **Conductivity Independence**:
Since conductivity is a property of the material and is independent of its dimensions, the new conductivity (σ') will remain the same as the original conductivity (σ).

5. **Conclusion**:
Therefore, the new conductivity σ' = σ.

### Final Answer:
The new conductivity of the conductor will be σ.

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