### Correct Option: A. Their resistance decreases with temperature ### Detailed Explanation: 1. **Understanding Resistance in Semiconductors**: - In semiconductors, the resistance is influenced by the number of charge carriers (electrons and holes) available to conduct electricity. At higher temperatures, more charge carriers are generated due to thermal excitation. 2. **Negative Temperature Coefficient of Resistance**: - A negative temperature coefficient of resistance means that as the temperature increases, the resistance of the material decreases. This is contrary to what happens in most metals, where resistance increases with temperature due to increased lattice vibrations that scatter electrons. 3. **Mechanism**: - In semiconductors, when the temperature rises, the thermal energy provided to the electrons allows more of them to jump from the valence band to the conduction band. This increases the number of free charge carriers available for conduction. - As the number of charge carriers increases, the material becomes more conductive, leading to a decrease in resistance. 4. **Mathematical Representation**: - The relationship can be expressed qualitatively as: \[ R(T) = \frac{V}{I} \] where \( R \) is resistance, \( V \) is voltage, and \( I \) is current. As temperature increases, \( I \) increases due to more charge carriers, leading to a decrease in \( R \). 5. **Example**: - Consider a silicon semiconductor. At room temperature, it has a certain resistance. If we heat it up, the resistance drops significantly because more electrons are excited into the conduction band, allowing more current to flow for the same applied voltage. ### Why Other Options Are Incorrect: - **Option B: The resistance increases with temperature**: - This statement is true for metals, where increased temperature leads to increased lattice vibrations, causing more scattering of electrons and thus higher resistance. However, it does not apply to semiconductors, which is why this option is incorrect. - **Option C: Their resistance is constantly changing with temperature**: - While it is true that the resistance of semiconductors changes with temperature, the term "constantly changing" is vague and does not specifically address the nature of the change (i.e., whether it increases or decreases). This option does not capture the essence of a negative temperature coefficient. - **Option D: They have electrons and holes at high temperature**: - While it is true that semiconductors have both electrons and holes, this statement does not directly relate to the concept of a negative temperature coefficient of resistance. The presence of holes and electrons is a characteristic of semiconductors, but it does not explain why their resistance decreases with temperature. ### Summary of Key Points: - **Negative Temperature Coefficient**: In semiconductors, resistance decreases as temperature increases. - **Charge Carriers**: Higher temperatures lead to more charge carriers (electrons and holes), enhancing conductivity. - **Contrast with Metals**: Unlike metals, where resistance increases with temperature, semiconductors behave oppositely. - **Practical Implication**: This property is crucial in applications like thermistors and temperature sensors, where resistance changes are used to measure temperature. This understanding is essential for grasping the behavior of semiconductors in various applications, especially in electronics and materials science.