Drift Velocity And Resistance - Ohm Law (Conductivity And Resistivity)

Drift velocity and resistance - Ohm’s Law (Conductivity and Resistivity)

Conductivity and resistivity are two important properties of a material that determine its electrical behavior.
The drift velocity of charge carriers is directly proportional to the applied electric field.
Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across it, at a constant temperature.
The resistance of a material is the ratio of the voltage across it to the current flowing through it.
The resistance of a conductor depends on its dimensions and material properties.
Resistivity is a measure of how strongly a material opposes the flow of current.
Conductivity is the reciprocal of resistivity and measures how easily a material conducts electric current.
Ohm’s Law can be expressed as: V = IR, where V is the voltage, I is the current, and R is the resistance. Slide 2

Drift Velocity

When an electric field is applied to a conductor, the free charge carriers (electrons or ions) experience a force that causes them to move.
The average velocity of these charge carriers is called the drift velocity.
It is important to note that the actual motion of individual electrons is random due to collisions with other particles. Slide 3

Relationship between Drift Velocity and Applied Electric Field

The drift velocity of charge carriers is directly proportional to the applied electric field.
Mathematically, we can express this relationship as: v = μE
- v represents the drift velocity,
- μ is the mobility of charge carriers, and
- E is the electric field strength. Slide 4

Ohm’s Law

Ohm’s Law relates the current flowing through a conductor to the voltage across it.
It can be stated as: V = IR
Here, V denotes the voltage, I represents the current, and R is the resistance. Slide 5

Resistance and Resistivity

Resistance is a measure of how much a material opposes the flow of electric current.
It is influenced by the dimensions and material properties of the conductor.
The resistance of a conductor can be calculated using the formula: R = ρl/A
- R denotes resistance,
- ρ is the resistivity of the material,
- l represents the length of the conductor, and
- A is the cross-sectional area of the conductor. Slide 6

Conductivity

Conductivity is a measure of how easily a material conducts electric current.
It is denoted by the symbol σ and is the reciprocal of resistivity.
Mathematically, conductivity can be expressed as: σ = 1/ρ Slide 7

Relation between Resistivity and Conductivity

Resistivity (ρ) and conductivity (σ) are inversely proportional to each other.
If a material has a high resistivity, it will have low conductivity, and vice versa. Slide 8

Conductors, Insulators, and Semiconductors

Conductors are materials that offer low resistance to the flow of electric current, such as metals.
Insulators are materials that offer high resistance and prevent the flow of electric current, like rubber or glass.
Semiconductors are materials whose conductivity lies between that of conductors and insulators.
The conductivity of semiconductors can be altered by various factors such as doping or temperature changes. Slide 9

Example: Calculating Resistance

Let’s consider a copper wire with a length of 2 meters and a radius of 0.5 mm.
The resistivity of copper is 1.68 x 10^-8 Ω.m.
We can calculate the resistance of the wire using the formula: R = ρl/A
- Given: l = 2 m, A = πr^2, r = 0.5 x 10^-3 m, ρ = 1.68 x 10^-8 Ω.m
- R = (1.68 x 10^-8 Ω.m) x (2 m) / (π x (0.5 x 10^-3 m)^2) Slide 10

Example: Calculating Resistance (continued)

Evaluating the expression, we find:
- R = (1.68 x 10^-8 Ω.m) x (2 m) / (π x (0.5 x 10^-3 m)^2)
- R = 0.034 Ω (approximately)
Thus, the resistance of the copper wire is approximately 0.034 Ω. Slide 11

Factors Affecting Resistance

The resistance of a material depends on several factors:
- Length of the conductor: Resistance increases with an increase in the length of the conductor.
- Cross-sectional area of the conductor: Resistance decreases with an increase in the cross-sectional area.
- Temperature: In most cases, resistance increases with an increase in temperature.
- Material properties: Each material has its unique resistivity that determines its resistance. Slide 12

Factors Affecting Conductivity

The conductivity of a material is influenced by:
- Presence of impurities: Impurities can either increase or decrease the conductivity of a material, depending on the type and concentration of impurities.
- Temperature: Generally, the conductivity of metals decreases with an increase in temperature due to increased scattering of free charge carriers. Slide 13

Ohm’s Law in Various Circuits

Ohm’s Law applies to various types of circuits:
- Simple circuits with a single resistor: V = IR, where V is the voltage, I is the current, and R is the resistance.
- Series circuits: The total resistance of series resistors is the sum of individual resistances, and the current is the same through each resistor.
- Parallel circuits: The total current in a parallel circuit is the sum of the currents through each branch, and the voltage across each resistor is the same. Slide 14

Electrical Power and Energy

Electrical power is the rate at which electrical energy is consumed or produced.
It can be calculated using the formula: P = IV, where P is power, I is current, and V is voltage.
The unit of power is the watt (W).
Electrical energy is the product of power and time, given by the equation: E = Pt, where E is energy, P is power, and t is time.
The unit of energy is the kilowatt-hour (kWh). Slide 15

Electric Current and the Human Body

Electric currents can pose risks to human health:
- High currents passing through the body can cause internal burns, muscle contractions, respiratory difficulties, and cardiac arrest.
- The severity of the shock depends on the current, the duration of contact, the path of the current, and the resistance of the body.
- Electrical safety measures should be followed to prevent accidents and injuries. Slide 16

Superconductivity

Superconductors are materials with zero electrical resistance at low temperatures.
Below a critical temperature, superconductors exhibit the Meissner effect and expel magnetic fields.
Superconductors have various applications, including in magnetic resonance imaging (MRI), particle accelerators, and power transmission. Slide 17

Thermistors and Temperature Measurement

Thermistors are temperature-sensitive resistors that exhibit a large change in resistance with temperature.
They can be used for temperature measurement and control in various applications.
The resistance of a thermistor decreases with an increase in temperature (negative temperature coefficient) or increases with an increase in temperature (positive temperature coefficient). Slide 18

Potential Difference and Electromotive Force (EMF)

Potential difference (V) is the electric potential energy difference per unit charge between two points in a circuit.
Electromotive force (EMF) is the electric potential energy per unit charge supplied by a source of electrical energy, such as a battery.
EMF is responsible for driving the electric current in a circuit.
It is important to note that EMF is not a force but rather a potential difference. Slide 19

Kirchhoff’s Laws

Kirchhoff’s laws are fundamental principles in circuit analysis:
- Kirchhoff’s first law, also known as the conservation of charge, states that the sum of currents entering a junction is equal to the sum of currents leaving the junction.
- Kirchhoff’s second law, also known as the voltage law, states that the algebraic sum of the electric potential differences in any closed loop of a circuit is zero. Slide 20

Applications of Ohm’s Law and Resistance

Ohm’s Law and the concept of resistance have numerous applications:
- Designing electrical circuits and calculating the appropriate resistors.
- Analyzing and troubleshooting electrical circuits.
- Determining the power consumed by electrical devices.
- Understanding the behavior of conductors and insulators.
- Developing technologies such as semiconductors and superconductors. Slide 21

Applications of Ohm’s Law and Resistance (continued)

Heat dissipation in electrical devices: The resistance of a conductor determines the amount of heat generated when current passes through it.
Building electrical circuits for various applications such as lighting, communication systems, and power distribution.
Developing electronic devices like computers, smartphones, and televisions.
Understanding the behavior of electric charge and current in various materials and environments.
Investigating the electrical properties of biological systems and medical applications. Slide 22

Example: Calculating Power

Let’s consider a light bulb with a resistance of 50 Ω and a current of 2 A flowing through it.
We can calculate the power consumed by the light bulb using the formula: P = IV
- Given: I = 2 A, V = IR = (2 A) x (50 Ω) Slide 23

Example: Calculating Power (continued)

Evaluating the expression, we find:
- P = IV = (2 A) x (50 Ω) = 100 W
Thus, the light bulb consumes 100 watts of power. Slide 24

Electric Shock and Safety Measures

Electric shocks can occur when a person comes into contact with an electric current.
Safety measures to prevent electric shocks include:
- Insulating equipment and electrical wiring.
- Grounding electrical circuits.
- Using circuit breakers and fuses to protect against overcurrent.
- Following safety procedures while handling electrical equipment.
- Avoiding contact with electrical sources when wet or in the presence of conductive materials. Slide 25

Factors Affecting the Electrical Resistance of Conductors

Temperature coefficient of resistance: Some materials have a positive or negative temperature coefficient, meaning their resistance changes with temperature.
Cross-sectional area and length: A thicker and shorter conductor has lower resistance compared to a thinner and longer conductor.
Temperature: Most conductors exhibit an increase in resistance with an increase in temperature.
Material properties: Different materials have different resistivities, which affect their resistance. Slide 26

Ohmic and Non-Ohmic Conductors

Ohmic conductors follow Ohm’s Law and have a linear relationship between the current and voltage.
Non-Ohmic conductors do not follow Ohm’s Law and may have a non-linear relationship between current and voltage.
Examples of non-Ohmic conductors include diodes, transistors, and gas discharge tubes. Slide 27

Power in Circuits

Power in a circuit can be calculated using different formulas based on the available variables:
- P = IV (for direct current)
- P = I^2R (for direct current)
- P = I^2R = V^2/R (for alternating current)
These formulas help us calculate the power consumed or produced by an electrical device or circuit. Slide 28

Series and Parallel Resistors

In series circuits:
- The total resistance is the sum of all individual resistances.
- The current is the same through each resistor.
- The voltage across each resistor depends on its resistance.
In parallel circuits:
- The total resistance is the reciprocal of the sum of the reciprocals of all individual resistances.
- The voltage across each resistor is the same.
- The total current is the sum of the currents through each resistor. Slide 29

Electrical Conductivity of Solutions

Some solutions can conduct electricity due to dissolved ions.
Electrolytes are substances that produce ions when dissolved in a solvent and can conduct electricity.
Strong electrolytes dissociate completely into ions, while weak electrolytes only partially dissociate.
Non-electrolytes do not produce ions and cannot conduct electricity.
The conductivity of a solution depends on the concentration of ions and temperature. Slide 30

Summary

Ohm’s Law relates current, voltage, and resistance in a conductor.
Drift velocity is the average velocity of charge carriers.
Resistance is determined by the dimensions and material properties of a conductor.
Resistivity and conductivity are properties that characterize a material’s resistance.
Factors affecting resistance include length, cross-sectional area, temperature, and material properties.
Ohm’s Law has various applications in circuit analysis, power calculations, and electronics.
Safety measures should be followed to prevent electric shocks.
Power in circuits can be calculated using different formulas.
Series and parallel circuits have distinct characteristics.
Electrolytes conduct electricity due to dissolved ions in a solution.