How does the resistivity of a conductor vary with temperature class 12?
2 Answers
In Class 12 physics, the resistivity of a conductor as a function of temperature is described by the following relationship:
\[ \rho(T) = \rho_0 \left[ 1 + \alpha(T - T_0) \right] \]
where:
- \(\rho(T)\) is the resistivity at temperature \(T\),
- \(\rho_0\) is the resistivity at a reference temperature \(T_0\),
- \(\alpha\) is the temperature coefficient of resistivity,
- \(T\) is the temperature in degrees Celsius or Kelvin.
**Key Points:**
1. **Positive Temperature Coefficient (\(\alpha\))**: For most conductors (like copper and aluminum), \(\alpha\) is positive. This means as the temperature increases, the resistivity of the conductor increases. This is because the increased thermal energy causes more frequent collisions between electrons and atoms, leading to higher resistance.
2. **Temperature Dependence**: The relationship shows a linear increase in resistivity with temperature for conductors. If the temperature coefficient is known, you can predict how resistivity will change with temperature.
3. **Graphical Representation**: A plot of resistivity versus temperature for a conductor will typically be a straight line with a positive slope if \(\alpha\) is positive.
This relationship helps in understanding and predicting how electrical components will behave under different temperature conditions.
\[ \rho(T) = \rho_0 \left[ 1 + \alpha(T - T_0) \right] \]
where:
- \(\rho(T)\) is the resistivity at temperature \(T\),
- \(\rho_0\) is the resistivity at a reference temperature \(T_0\),
- \(\alpha\) is the temperature coefficient of resistivity,
- \(T\) is the temperature in degrees Celsius or Kelvin.
**Key Points:**
1. **Positive Temperature Coefficient (\(\alpha\))**: For most conductors (like copper and aluminum), \(\alpha\) is positive. This means as the temperature increases, the resistivity of the conductor increases. This is because the increased thermal energy causes more frequent collisions between electrons and atoms, leading to higher resistance.
2. **Temperature Dependence**: The relationship shows a linear increase in resistivity with temperature for conductors. If the temperature coefficient is known, you can predict how resistivity will change with temperature.
3. **Graphical Representation**: A plot of resistivity versus temperature for a conductor will typically be a straight line with a positive slope if \(\alpha\) is positive.
This relationship helps in understanding and predicting how electrical components will behave under different temperature conditions.