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 1: Understand the properties of resistivity in conductors and semiconductors
- **Copper (Cu)** is a metal and behaves as a conductor. Its resistivity decreases with a decrease in temperature.
- **Germanium (Ge)** is a semiconductor. Its resistivity increases with a decrease in temperature.

### Step 2: Analyze the effect of cooling on resistivity
- When the temperature of copper is decreased, the resistivity (ρ) of copper decreases. This is because the number of charge carriers (free electrons) in metals increases as temperature decreases, leading to lower resistivity.
- Conversely, when the temperature of germanium is decreased, the resistivity increases. In semiconductors, cooling reduces the thermal energy available to excite electrons across the band gap, thus reducing the number of charge carriers and increasing resistivity.

### Step 3: Summarize the changes in resistivity
- For copper (Cu): As temperature decreases, resistivity decreases (ρ_Cu decreases).
- For germanium (Ge): As temperature decreases, resistivity increases (ρ_Ge increases).

### Step 4: Conclusion
- Therefore, when identical pieces of germanium and copper are cooled, the resistivity of copper will be less than that of germanium.

### Final Answer
The resistivity of copper decreases while the resistivity of germanium increases when both are cooled.

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