The resistance of germanium `"_______"` with rise in temperature.

Options

A. increases
B. decreases
C. remains the same
D. first increases then decreases

Answer

To determine how the resistance of germanium changes with an increase in temperature, we can follow these steps:

### Step 1: Understand the relationship between resistance and temperature
The resistance \( R \) of a material can be expressed using the formula:
\[ R = R_0 \left( 1 + \alpha (T - T_0) \right) \]
where:
- \( R_0 \) is the initial resistance at temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistance,
- \( T \) is the final temperature.

### Step 2: Identify the temperature coefficient for germanium
For germanium, the temperature coefficient \( \alpha \) is negative. This means that as the temperature increases, the effect of \( \alpha (T - T_0) \) becomes more negative.

### Step 3: Analyze the effect of increasing temperature
As the temperature \( T \) increases:
- The term \( (T - T_0) \) becomes larger,
- Since \( \alpha \) is negative, \( \alpha (T - T_0) \) becomes more negative.

### Step 4: Determine the change in resistance
Substituting the negative value of \( \alpha \) into the equation:
\[ R = R_0 \left( 1 + \text{(more negative value)} \right) \]
This indicates that the overall value of \( R \) decreases as the temperature increases.

### Conclusion
Therefore, the resistance of germanium **decreases** with an increase in temperature.

### Final Answer
The resistance of germanium **decreases** with rise in temperature.

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