Home
Class 12
PHYSICS
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. A current of 1 A flows through a copper wire. The number of electrons passing through any cross-section of the wire in 1.6 sec is (charge of a electron = 1.6 xx 10^(-19 c)`.

A

`10^(25)`

B

`10^(19)`

C

`10^(25)`

D

`10^(28)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the number of electrons passing through a copper wire in 1.6 seconds when a current of 1 A flows through it, we can follow these steps: ### Step 1: Understand the relationship between current, charge, and time. The current (I) flowing through a conductor is defined as the charge (Q) passing through a cross-section of the conductor per unit time (t). Mathematically, this is expressed as: \[ I = \frac{Q}{t} \] ### Step 2: Rearrange the formula to find charge. From the equation above, we can rearrange it to find the total charge that passes through the wire in time \( t \): \[ Q = I \times t \] ### Step 3: Substitute the values for current and time. Given: - Current, \( I = 1 \, \text{A} \) - Time, \( t = 1.6 \, \text{s} \) Substituting these values into the equation: \[ Q = 1 \, \text{A} \times 1.6 \, \text{s} = 1.6 \, \text{C} \] ### Step 4: Calculate the number of electrons. The charge of a single electron (e) is given as \( 1.6 \times 10^{-19} \, \text{C} \). To find the number of electrons (n) that corresponds to the total charge (Q), we can use the formula: \[ n = \frac{Q}{e} \] ### Step 5: Substitute the values for charge and electron charge. Substituting the values: \[ n = \frac{1.6 \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \] ### Step 6: Perform the calculation. Calculating the above expression: \[ n = \frac{1.6}{1.6 \times 10^{-19}} = 10^{19} \] ### Conclusion: Thus, the number of electrons passing through any cross-section of the copper wire in 1.6 seconds is: \[ n = 10^{19} \] ---
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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. If no potential difference is maintained between the ends of a conductor

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. A constant potential difference is maintained between the ends of a conductor having nonuniform cross-section. Which of the following quantities will not change along the length of the conductor

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. A uniform wire of length 2.0 m and cross-sectional area 10^(-7) m^(2) carries a current of 1.6 A. If there are 10^(28) free electrons per m in copper, the drift speed of electrons in copper is

In diamond, the number of free electrons are:

A current of 4 A is flowing in a cylindrical conductor. The number of free electrons passing per second through the cross-section of conductor is

A substance with less number of free electrons is said to be good conductor.

Mobility of free electrons in a conductor is

If n ,e,m and tau are free electron density in conductor , charge of electron, mass of electron and relaxation time of free electrons , then resistivity rho of the conductor can be expressed as