Which of the following quantities do not change when a resistor connected to a battery is heated due to the current?

Options

A. (a)Drift speed
B. (b)Resistivity
C. (c )Resistance
D. (d)Number of free electrons

Answer

To solve the question of which quantity does not change when a resistor connected to a battery is heated due to the current, we will analyze each of the given options step by step.

### Step 1: Understand the effect of heating on a resistor
When a resistor carries current, it heats up due to the electrical energy being converted into thermal energy. This heating affects various properties of the resistor.

### Step 2: Analyze the options
1. **Drift Speed (vd)**: The drift speed of charge carriers in a conductor is given by the equation \( I = nEAq \), where \( I \) is the current, \( n \) is the number density of charge carriers, \( A \) is the cross-sectional area, and \( q \) is the charge of the carriers. As the resistor heats up, the resistance increases, which leads to a decrease in current (assuming the voltage remains constant). Since drift speed is directly related to current, the drift speed will also decrease. Therefore, drift speed changes.

2. **Resistivity (ρ)**: The resistivity of a material is a property that can change with temperature. For most conductors, resistivity increases with temperature. Therefore, as the resistor heats up, the resistivity will also change.

3. **Resistance (R)**: The resistance of a resistor is given by the formula \( R = \frac{\rho L}{A} \). Since we have established that resistivity changes with temperature, and the dimensions (length \( L \) and area \( A \)) of the resistor remain constant, the resistance will also change as the resistivity changes.

4. **Number of Electrons (n)**: The number of charge carriers (electrons) in a given volume of the conductor does not change when the resistor is heated. The total number of electrons is a property of the material and its dimensions, which remain constant regardless of the temperature.

### Conclusion
From the analysis, we find that:
- Drift speed changes.
- Resistivity changes.
- Resistance changes.
- The number of electrons does not change.

Thus, the quantity that does not change when a resistor connected to a battery is heated due to the current is **the number of electrons**.

### Final Answer
The answer is **Option D: Number of Electrons**.

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