The temperature (T) dependence of resistivity (rho) of a semiconductor is represented by :

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the temperature dependence of resistivity (ρ) of a semiconductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Conductivity and Resistivity**:
- The conductivity (σ) of a semiconductor increases with temperature. This is a key property of semiconductors.
- The resistivity (ρ) is inversely proportional to conductivity:
\[ \rho = \frac{1}{\sigma} \]

2. **Establish the Temperature Dependence**:
- As the temperature (T) increases, the conductivity (σ) increases. Therefore, the resistivity (ρ) must decrease.
- This can be expressed mathematically as:
\[ \sigma \propto T \quad \text{(as T increases, σ increases)} \]
- Consequently, we can say:
\[ \rho \propto \frac{1}{T} \quad \text{(as T increases, ρ decreases)} \]

3. **Formulate the Relationship**:
- From the above relationship, we can derive that:
\[ T \cdot \rho = \text{constant} \]
- This implies that the product of temperature and resistivity remains constant for a semiconductor.

4. **Graphical Representation**:
- The relationship \( T \cdot \rho = \text{constant} \) indicates that if you plot resistivity (ρ) on the y-axis and temperature (T) on the x-axis, the graph will be a rectangular hyperbola.
- This is because as one variable increases, the other decreases, maintaining a constant product.

5. **Conclusion**:
- Therefore, the correct representation of the temperature dependence of resistivity in a semiconductor is that it forms a rectangular hyperbola.

### Final Answer:
The temperature dependence of resistivity (ρ) of a semiconductor is represented by a rectangular hyperbola.

---