Which graph best represent the relationship between conductivity and resistivity for a solid ?

Options

A.
B.
C.
D.

Explanation

To determine the relationship between conductivity and resistivity for a solid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Conductivity (σ) is a measure of a material's ability to conduct electric current.
- Resistivity (ρ) is a measure of how strongly a material opposes the flow of electric current.

2. **Establish the Relationship**:
- The relationship between conductivity and resistivity is given by the formula:
\[ \sigma = \frac{1}{\rho} \]
- This indicates that conductivity is inversely proportional to resistivity.

3. **Analyze the Implications**:
- If resistivity (ρ) increases, conductivity (σ) decreases, and vice versa.
- This means that as you plot conductivity on the x-axis and resistivity on the y-axis, the graph will show a hyperbolic relationship.

4. **Graphical Representation**:
- The relationship can be expressed as:
\[ \sigma \cdot \rho = 1 \]
- Rearranging this gives us:
\[ \rho = \frac{1}{\sigma} \]
- This indicates that the graph will be a hyperbola, where as conductivity increases, resistivity decreases.

5. **Identify the Correct Graph**:
- Given the options A, B, C, and D, we need to find the graph that represents a hyperbolic curve.
- Upon examining the options, option C represents this hyperbolic relationship correctly.

6. **Conclusion**:
- Therefore, the graph that best represents the relationship between conductivity and resistivity for a solid is option C.