The temperature dependence of resistance of Cu and undoped Si in the temperature range `300 -400 K, ` is best described by :

Options

A. Linear increase for Cu, exponential increase for Si.
B. Linear increase for Cu, exponential decrease for Si.
C. Linear decrease for Cu, linear decrease for Si.
D. Linear increase for Cu, linear increase for Si.

Answer

To solve the problem regarding the temperature dependence of resistance for copper (Cu) and undoped silicon (Si) in the temperature range of 300 K to 400 K, we need to analyze the behavior of metals and semiconductors with respect to temperature changes.

### Step-by-step Solution:

1. **Identify the Material Types**:
- Copper (Cu) is a metal.
- Undoped silicon (Si) is a semiconductor.

2. **Understand the Behavior of Metals**:
- In metals, as the temperature increases, the resistance also increases. This is due to the increased thermal agitation of the lattice ions, which leads to more frequent collisions of conduction electrons.
- The relationship can be described as:
\[ R(T) = R_0(1 + \alpha(T - T_0)) \]
where \( R_0 \) is the resistance at a reference temperature \( T_0 \), and \( \alpha \) is the temperature coefficient of resistance.

3. **Graphical Representation for Copper**:
- Plotting resistance (R) against temperature (T) for copper will yield a linear graph, indicating a direct proportionality between resistance and temperature in this range.

4. **Understand the Behavior of Semiconductors**:
- In semiconductors like silicon, as the temperature increases, the number of charge carriers (electrons and holes) increases significantly due to thermal excitation. This leads to a decrease in resistance.
- The relationship can be described as:
\[ R(T) \propto \frac{1}{n(T)} \]
where \( n(T) \) is the charge carrier density, which increases with temperature.

5. **Graphical Representation for Silicon**:
- Plotting resistance (R) against temperature (T) for silicon will yield a curve that decreases exponentially, indicating that resistance decreases as temperature increases.

6. **Conclusion**:
- Therefore, the temperature dependence of resistance can be summarized as:
- For copper: Linear increase in resistance with temperature.
- For silicon: Exponential decrease in resistance with temperature.

### Final Answer:
The temperature dependence of resistance of Cu and undoped Si in the temperature range 300 K to 400 K is best described by a linear increase for copper and an exponential decrease for silicon.