The temperature coefficient of resistance of an alloy used for making resistor is

Options

A. small and positive
B. small and negative
C. large and positive
D. large and negative

Answer

To solve the question regarding the temperature coefficient of resistance of an alloy used for making resistors, we can follow these steps:

### Step 1: Understand the concept of temperature coefficient of resistance
The temperature coefficient of resistance (α) indicates how much the resistance of a material changes with temperature. It is defined as the fractional change in resistance per degree change in temperature.

### Step 2: Recall the formula for resistance variation
The formula for the variation of resistance with temperature is given by:
\[ R = R_0 (1 + \alpha \Delta T) \]
where:
- \( R \) is the resistance at temperature \( T \),
- \( R_0 \) is the resistance at a reference temperature (usually 0°C),
- \( \alpha \) is the temperature coefficient of resistance,
- \( \Delta T \) is the change in temperature.

### Step 3: Analyze the behavior of resistance with temperature
From the formula, if \( \Delta T \) is positive (meaning the temperature increases), the term \( \alpha \Delta T \) will also be positive if \( \alpha \) is positive. This indicates that the resistance \( R \) will increase with an increase in temperature.

### Step 4: Determine the desired characteristics of the temperature coefficient
In practical applications, especially in resistors, we want the resistance to remain relatively stable with temperature changes. Therefore, we prefer a small value of \( \alpha \) so that the resistance does not vary significantly with temperature changes.

### Step 5: Conclusion
Based on the analysis, we conclude that the temperature coefficient of resistance for an alloy used for making resistors should be small and positive. This ensures that the resistance increases slightly with temperature but does not vary drastically, which could lead to equipment failure.

### Final Answer
The temperature coefficient of resistance of an alloy used for making resistors is small and positive.

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