**NCERT Chapter 3 Current Electricity**

NCERT Chapter 3, “Current Electricity,” introduces the concept of electric current and how it flows through a circuit. It discusses the relationship between electric current, voltage, and resistance, as well as the basic laws that govern the flow of electric current.

The chapter also covers practical applications of electric current, such as the use of electric meters to measure the amount of current flowing through a circuit. Additionally, the chapter discusses the dangers of electric current and how to safely work with it.

## Introduction of Current Electricity

Current electricity is the study of the flow of electric charge through materials that are capable of conducting electricity. Electric current is the movement of electrons through a conductor, such as a metal wire. The flow of electric current is driven by a difference in electric potential, also known as voltage, between two points in a circuit. The resistance of a material to the flow of electric current is measured in ohms.

The basic laws that govern the flow of electric current are Ohm’s law, which states that the current flowing through a conductor is directly proportional to the voltage applied to it and inversely proportional to the resistance of the conductor, and Kirchhoff’s laws, which describe the conservation of electric charge and energy in a circuit.

Electric current has many practical applications, including the generation and distribution of electrical power, the operation of electronic devices, and the transmission of information through telecommunications. However, it is important to use caution when working with electric current, as it can be dangerous and potentially lethal.

## Electric Current

Electric current is the flow of electric charge through a conductor, such as a metal wire. It is measured in units of amperes (A) or milliamperes (mA). The direction of the electric current is determined by the direction of the flow of electric charge. In most materials, electric current is carried by the movement of electrons, which are negatively charged particles.

Electric current is an important concept in electricity and electronics. It is used to power electric devices and appliances, transmit information through telecommunications systems, and perform many other tasks. Electric current is typically generated by the movement of electric charge through a conductor due to a difference in electric potential, or voltage, between two points in a circuit. The flow of electric current through a conductor is governed by Ohm’s law, which states that the current is directly proportional to the voltage applied to it and inversely proportional to the resistance of the conductor.

### Electric current Formula

The formula for electric current is:

I = Q/t

where:

I is the electric current, measured in amperes (A) Q is the electric charge, measured in coulombs (C) t is the time interval over which the charge flows, measured in seconds (s)

The electric current is a measure of the rate at which electric charge flows through a conductor. It is equal to the amount of electric charge that passes through a conductor per second. The electric current can be calculated by dividing the amount of electric charge that flows through a conductor by the time interval over which the charge flows.

For example, if a charge of 10 coulombs flows through a conductor in 5 seconds, the electric current would be:

I = Q/t = 10 C / 5 s = 2 A

Electric current is an important concept in electricity and electronics, as it is used to power electric devices and appliances, transmit information through telecommunications systems, and perform many other tasks.

### Example with Solution

Here is an example problem demonstrating the use of Ohm’s law:

A circuit has a resistance of 10 ohms and a voltage of 20 volts applied to it. What is the electric current flowing through the circuit?

To solve this problem, we can use the formula for Ohm’s law:

I = V/R = 20 V / 10 Ω = 2 A

Therefore, the electric current flowing through the circuit is 2 amperes.

Another example:

A circuit has an electric current of 5 amperes and a resistance of 2 ohms. What is the voltage applied to the circuit?

To solve this problem, we can use the formula for Ohm’s law:

V = I * R = 5 A * 2 Ω = 10 V

Therefore, the voltage applied to the circuit is 10 volts.

## Electric Currents in Conductors

Electric current is the flow of electric charge through a conductor, such as a metal wire. It is measured in units of amperes (A) or milliamperes (mA). The direction of the electric current is determined by the direction of the flow of electric charge. In most materials, electric current is carried by the movement of electrons, which are negatively charged particles.

### Formula

The formula for electric current is:

I = Q/t

where:

I is the electric current, measured in amperes (A) Q is the electric charge, measured in coulombs (C) t is the time interval over which the charge flows, measured in seconds (s)

The electric current is a measure of the rate at which electric charge flows through a conductor. It is equal to the amount of electric charge that passes through a conductor per second. The electric current can be calculated by dividing the amount of electric charge that flows through a conductor by the time interval over which the charge flows.

### Example with Solution

For example, if a charge of 10 coulombs flows through a conductor in 5 seconds, the electric current would be:

I = Q/t = 10 C / 5 s = 2 A

Here is an example problem demonstrating the use of the formula for electric current:

A conductor carries a charge of 8 coulombs in 2 seconds. What is the electric current flowing through the conductor?

To solve this problem, we can use the formula for electric current:

I = Q/t = 8 C / 2 s = 4 A

Therefore, the electric current flowing through the conductor is 4 amperes.

## Ohm’s Law

Ohm’s law is a fundamental relationship in electricity that describes the relationship between electric current, voltage, and resistance. It states that the current flowing through a conductor is directly proportional to the voltage applied to it and inversely proportional to the resistance of the conductor.

### Formula

The formula for Ohm’s law is:

I = V/R

where:

I is the electric current, measured in amperes (A) V is the voltage, measured in volts (V) R is the resistance, measured in ohms (Ω)

Ohm’s law can be used to predict the behavior of an electric circuit under different conditions. For example, if the resistance of a conductor is known and the voltage applied to it is changed, Ohm’s law can be used to calculate the resulting change in electric current. Similarly, if the resistance and current are known, Ohm’s law can be used to calculate the voltage required to produce a desired current.

### Example & Solution

Here is an example problem demonstrating the use of Ohm’s law:

A circuit has a resistance of 10 ohms and a voltage of 20 volts applied to it. What is the electric current flowing through the circuit?

To solve this problem, we can use the formula for Ohm’s law:

I = V/R = 20 V / 10 Ω = 2 A

Therefore, the electric current flowing through the circuit is 2 amperes.

Another example:

A circuit has an electric current of 5 amperes and a resistance of 2 ohms. What is the voltage applied to the circuit?

To solve this problem, we can use the formula for Ohm’s law:

V = I * R = 5 A * 2 Ω = 10 V

Therefore, the voltage applied to the circuit is 10 volts.

## Drift of Electrons and the Origin of Resistivity

The drift of electrons refers to the movement of electrons through a conductor due to an applied electric field. When an electric field is applied to a conductor, it causes the electrons in the conductor to move in the direction of the field. This movement of electrons is known as the drift of electrons.

The drift of electrons is the origin of resistivity, which is the property of a material that determines its resistance to the flow of electric current. Materials that have a high resistivity, such as rubber and glass, have a greater resistance to the flow of electric current and are therefore not good conductors. Materials that have a low resistivity, such as copper and silver, have a lower resistance to the flow of electric current and are therefore good conductors.

The resistivity of a material is determined by the number of free electrons it has, as well as the mobility of these electrons. Materials with a large number of free electrons and high mobility will have a low resistivity, while materials with a small number of free electrons and low mobility will have a high resistivity.

The drift of electrons is an important concept in electricity and electronics, as it is the basis for the flow of electric current through a conductor. Understanding the drift of electrons can help in the design and analysis of electrical circuits and devices.

### Formula

There is no specific formula for the drift of electrons or the origin of resistivity. The drift of electrons refers to the movement of electrons through a conductor due to an applied electric field, while resistivity is the property of a material that determines its resistance to the flow of electric current.

The resistivity of a material is typically represented by the Greek letter ρ (rho) and is measured in units of ohm-meters (Ω⋅m). The formula for resistivity is:

ρ = R/l

where:

ρ is the resistivity of the material, measured in ohm-meters (Ω⋅m) R is the resistance of a conductor of the material, measured in ohms (Ω) l is the length of the conductor, measured in meters (m) A is the cross-sectional area of the conductor, measured in square meters (m²)

The resistivity of a material can be calculated by measuring the resistance of a conductor made of the material and dividing it by the length and cross-sectional area of the conductor.

For example, if a copper wire has a resistance of 1 ohm and a length of 2 meters with a cross-sectional area of 1 square meter, the resistivity of the copper wire would be:

ρ = R/l/A = 1 Ω / 2 m / 1 m² = 0.5 Ω⋅m

### Examples & Solutions

Here are a few examples demonstrating the concepts of drift of electrons and resistivity:

*Example 1:*

Consider a copper wire with a resistance of 2 ohms and a length of 1 meter. The cross-sectional area of the wire is 0.5 square meters. What is the resistivity of the copper wire?

To solve this problem, we can use the formula for resistivity:

ρ = R/l/A = 2 Ω / 1 m / 0.5 m² = 4 Ω⋅m

Therefore, the resistivity of the copper wire is 4 ohm-meters.

*Example 2:*

An electric field is applied to a conductor made of a material with a resistivity of 10 ohm-meters. The electric field causes the electrons in the conductor to drift at a velocity of 5 x 10^5 meters per second. How long does it take for an electron to drift a distance of 1 meter in the conductor?

To solve this problem, we can use the formula for velocity:

v = d/t

where v is the velocity of the electron, d is the distance traveled by the electron, and t is the time it takes for the electron to travel the distance.

We can rearrange the formula to solve for t:

t = d/v

Substituting the given values, we get:

t = 1 m / 5 x 10^5 m/s = 2 x 10^-6 s

Therefore, it takes 2 microseconds for an electron to drift a distance of 1 meter in the conductor.

### Additional Key Points about ‘Drift of Electrons and the Origin of Resistivity’

Here are some additional key points about the drift of electrons and the origin of resistivity:

- The drift of electrons is the movement of electrons through a conductor due to an applied electric field. It is the basis for the flow of electric current through a conductor.
- The resistivity of a material is the property that determines its resistance to the flow of electric current. Materials with a high resistivity, such as rubber and glass, have a greater resistance to the flow of electric current and are therefore not good conductors. Materials with a low resistivity, such as copper and silver, have a lower resistance to the flow of electric current and are therefore good conductors.
- The resistivity of a material is determined by the number of free electrons it has and the mobility of these electrons. Materials with a large number of free electrons and high mobility will have a low resistivity, while materials with a small number of free electrons and low mobility will have a high resistivity.
- The resistivity of a material can be calculated by measuring the resistance of a conductor made of the material and dividing it by the length and cross-sectional area of the conductor.
- The drift of electrons and the concept of resistivity are important in the design and analysis of electrical circuits and devices. Understanding these concepts can help in predicting the behavior of an electric circuit under different conditions and in determining the appropriate materials to use in a given application.

## Mobility

Mobility is a measure of the ability of charge carriers (such as electrons or holes) to move through a material under the influence of an electric field. The mobility of charge carriers is an important property of a material and plays a significant role in determining its electrical conductivity.

The mobility of charge carriers is typically represented by the Greek letter μ (mu) and is measured in units of square meters per volt-second (m²/V⋅s). The formula for mobility is:

μ = J/E

where:

μ is the mobility of the charge carriers, measured in square meters per volt-second (m²/V⋅s) J is the electric current density, measured in amperes per square meter (A/m²) E is the electric field strength, measured in volts per meter (V/m)

The mobility of charge carriers can be calculated by dividing the electric current density by the electric field strength.

The mobility of charge carriers is an important parameter in determining the electrical conductivity of a material. Materials with high mobility of charge carriers will have a high electrical conductivity, while materials with low mobility of charge carriers will have a low electrical conductivity.

For example, metals typically have a high mobility of charge carriers due to their large number of free electrons, which allows them to easily move through the material under the influence of an electric field. As a result, metals have a high electrical conductivity and are good conductors of electricity.

### SI Unit of Mobility

- The SI unit of mobility is m
^{2}/Vs.

The mobility of charge carriers is typically measured in units of square meters per volt-second (m²/V⋅s). This unit is used to express the ability of charge carriers to move through a material under the influence of an electric field.

The mobility of charge carriers is an important property of a material and plays a significant role in determining its electrical conductivity. Materials with high mobility of charge carriers will have a high electrical conductivity, while materials with low mobility of charge carriers will have a low electrical conductivity.

For example, metals typically have a high mobility of charge carriers due to their large number of free electrons, which allows them to easily move through the material under the influence of an electric field. As a result, metals have a high electrical conductivity and are good conductors of electricity.

In contrast, non-metallic materials such as rubber and glass have a low mobility of charge carriers and are poor conductors of electricity.

### Formula

The formula for mobility is:

μ = J/E

where:

μ is the mobility of the charge carriers, measured in square meters per volt-second (m²/V⋅s) J is the electric current density, measured in amperes per square meter (A/m²) E is the electric field strength, measured in volts per meter (V/m)

The mobility of charge carriers can be calculated by dividing the electric current density by the electric field strength. The formula for mobility allows you to determine the ability of charge carriers to move through a material under the influence of an electric field.

For example, if the electric current density in a material is 10 amperes per square meter and the electric field strength is 5 volts per meter, the mobility of the charge carriers in the material would be:

μ = J/E = 10 A/m² / 5 V/m = 2 m²/V⋅s

### Examples & Solutions

Here are a few examples demonstrating the use of the formula for mobility:

#### Example 1:

A conductor has an electric current density of 8 amperes per square meter and an electric field strength of 2 volts per meter. What is the mobility of the charge carriers in the conductor?

To solve this problem, we can use the formula for mobility:

μ = J/E = 8 A/m² / 2 V/m = 4 m²/V⋅s

Therefore, the mobility of the charge carriers in the conductor is 4 square meters per volt-second.

#### Example 2:

A conductor has a mobility of 6 square meters per volt-second and an electric field strength of 3 volts per meter. What is the electric current density in the conductor?

To solve this problem, we can use the formula for mobility:

J = μ * E = 6 m²/V⋅s * 3 V/m = 18 A/m²

Therefore, the electric current density in the conductor is 18 amperes per square meter.

### Additional Key Points about Mobility

Here are some additional key points about mobility:

- Mobility is a measure of the ability of charge carriers (such as electrons or holes) to move through a material under the influence of an electric field.
- The mobility of charge carriers is typically represented by the Greek letter μ (mu) and is measured in units of square meters per volt-second (m²/V⋅s).
- The mobility of charge carriers is an important property of a material and plays a significant role in determining its electrical conductivity. Materials with high mobility of charge carriers will have a high electrical conductivity, while materials with low mobility of charge carriers will have a low electrical conductivity.
- The mobility of charge carriers can be calculated by dividing the electric current density by the electric field strength.
- The mobility of charge carriers is an important parameter in determining the electrical conductivity of a material. It is used in the analysis and design of electrical circuits and devices, and in the selection of materials for use in electrical and electronic applications.