Question

Give the relationship of temperature with the resistance and resistivity of a conductor. Define the temperature coefficient of the resistance and give its unit.

Hint:

The resistance and resistivity of most materials increase with temperature. The temperature coefficient of resistance determines the rate of this change.

Answer 1

Step 1: Relationship Between Temperature and Resistance.
The resistance \( R \) of a conductor at a temperature \( T \) is related to its resistance at a reference temperature \( T_0 \) by: \[ R = R_0 (1 + \alpha (T - T_0)) \] where: - \( R_0 \) is the resistance at the reference temperature \( T_0 \), - \( \alpha \) is the temperature coefficient of resistance, - \( T \) is the temperature.
Step 2: Relationship Between Temperature and Resistivity.
The resistivity \( \rho \) of a conductor also depends on temperature, and it is given by: \[ \rho = \rho_0 (1 + \alpha (T - T_0)) \] where: - \( \rho_0 \) is the resistivity at the reference temperature \( T_0 \).
Step 3: Temperature Coefficient of Resistance.
The temperature coefficient of resistance \( \alpha \) is a constant that indicates how much the resistance changes with temperature. It is defined as: \[ \alpha = \frac{1}{R_0} \frac{dR}{dT} \] Its unit is \( \text{°C}^{-1} \).