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In a metal in the solid state, such as a...

In a metal in the solid state, such as a copper wire, the atoms are strongly bound to one another and occupý fixed positions. Some electrons (called the conductor electrons) are free to move in the body of the metal while the other are strongly bound to their atoms. In good conductors, the number of free electrons is very large of the order of `10^(28)` electrons per cubic metre in copper. The free electrons are in random motion and keep colliding with atoms. At room temperature, they move with velocities of the order of `10^5` m/s. These velocities are completely random and there is not net flow of charge in any directions. If a potential difference is maintained between the ends of the metal wire (by connecting it across a battery), an electric field is set up which accelerates the free electrons: These accelerated electrons frequently collide with the atoms of the conductor, as a result, they acquire a constant speed called the drift speed which is given by `V_e =` 1/enA where I = current in the conductor due to drifting electrons, e = charge of electron, n = number of free electrons per unit volume of the conductor and A = area of cross-section of the conductor. The drift speed of free electrons in a conductor depends upon

A

the material of the conductor

B

the temperature of the conductor

C

the potential difference applied across the ends of the conductor

D

the area of cross-section of the conductor

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To determine the factors on which the drift speed of free electrons in a conductor depends, we can analyze the given formula for drift speed: \[ V_d = \frac{I}{n e A} \] Where: - \( V_d \) = drift speed - \( I \) = current in the conductor - \( n \) = number of free electrons per unit volume of the conductor - \( e \) = charge of an electron - \( A \) = area of cross-section of the conductor ### Step 1: Analyze the formula for drift speed The drift speed \( V_d \) is directly proportional to the current \( I \) and inversely proportional to the product of \( n \), \( e \), and \( A \). ### Step 2: Identify the variables 1. **Material of the conductor (n)**: The number of free electrons per unit volume \( n \) varies with the material. Different materials have different numbers of free electrons available for conduction. 2. **Temperature**: While the drift speed formula does not explicitly include temperature, the number of free electrons \( n \) can be affected by temperature. However, the drift speed itself does not depend directly on temperature in the formula. 3. **Potential difference**: The current \( I \) is influenced by the potential difference applied across the conductor. Thus, indirectly, the drift speed depends on the potential difference. 4. **Area of cross-section (A)**: The drift speed is inversely proportional to the area of cross-section \( A \). A larger area results in a smaller drift speed for a given current. ### Step 3: Conclusion on dependencies Based on the analysis: - The drift speed depends on: - The material of the conductor (due to \( n \)) - The potential difference (indirectly through \( I \)) - The area of cross-section (inversely through \( A \)) - The drift speed does not depend on temperature directly. ### Final Answer The drift speed of free electrons in a conductor depends on: 1. The material of the conductor (due to the number of free electrons, \( n \)). 2. The potential difference applied across the conductor (indirectly through current, \( I \)). 3. The area of cross-section of the conductor (inversely related).
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In a metal in the solid state, such as a copper wire, the atoms are strongly bound to one another and occupý fixed positions. Some electrons (called the conductor electrons) are free to move in the body of the metal while the other are strongly bound to their atoms. In good conductors, the number of free electrons is very large of the order of 10^(28) electrons per cubic metre in copper. The free electrons are in random motion and keep colliding with atoms. At room temperature, they move with velocities of the order of 10^5 m/s. These velocities are completely random and there is not net flow of charge in any directions. If a potential difference is maintained between the ends of the metal wire (by connecting it across a battery), an electric field is set up which accelerates the free electrons: These accelerated electrons frequently collide with the atoms of the conductor, as a result, they acquire a constant speed called the drift speed which is given by V_e = 1/enA where I = current in the conductor due to drifting electrons, e = charge of electron, n = number of free electrons per unit volume of the conductor and A = area of cross-section of the conductor. Choose the current statements

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