Identical pieces of Ge and Cu are taken and cooled then

Options

A. Resistivity of both increase
B. Resistivity of both decrease
C. Resistivity of Cu increases and Ge decreases
D. Resistivity of Cu decreases and Ge increases

Answer

To solve the question regarding the resistivity of identical pieces of germanium (Ge) and copper (Cu) when cooled, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Materials**:
- We have two materials: germanium (Ge) which is a semiconductor, and copper (Cu) which is a metal.

2. **Understand Temperature Coefficients**:
- Metals like copper have a **positive temperature coefficient of resistivity**. This means that as the temperature decreases, the resistivity of copper also decreases.
- Semiconductors like germanium have a **negative temperature coefficient of resistivity**. This means that as the temperature decreases, the resistivity of germanium increases.

3. **Write the Resistivity Equations**:
- For copper, the resistivity can be expressed as:
\[ \rho_{Cu} = \rho_{0} (1 + \alpha_{Cu} \Delta T) \]
where \(\alpha_{Cu}\) is positive, and \(\Delta T\) is negative (since we are cooling).
- For germanium, the resistivity can be expressed as:
\[ \rho_{Ge} = \rho_{0} (1 - \alpha_{Ge} \Delta T) \]
where \(\alpha_{Ge}\) is negative, and \(\Delta T\) is also negative.

4. **Analyze the Effects of Cooling**:
- As the temperature decreases (\(\Delta T < 0\)):
- For copper:
\[ \rho_{Cu} \text{ decreases because } \alpha_{Cu} \Delta T \text{ is negative.} \]
- For germanium:
\[ \rho_{Ge} \text{ increases because } -\alpha_{Ge} \Delta T \text{ is positive.} \]

5. **Conclusion**:
- Therefore, when cooled:
- The resistivity of copper decreases.
- The resistivity of germanium increases.

6. **Final Answer**:
- The correct statement is that the resistivity of copper decreases while the resistivity of germanium increases.