Mobility And Temperature Dependence Of Resistivity- Current And Electricity

Slide 1: Mobility and Temperature Dependence of Resistivity

Resistivity ($\rho$) is a measure of how strongly a material opposes the flow of electric current.
The mobility of charge carriers in a material determines the resistivity.
Mobility ($\mu$) is the characteristic of a material that describes how easily charge carriers move through it.
Resistivity and Mobility are related by the equation:
- $\rho = \frac{1}{n \cdot e \cdot \mu}$
- Where $n$ is the charge carrier density and $e$ is the charge of the carrier.

Slide 2: Temperature Dependence of Resistivity

The resistivity of most materials increases with temperature.
This can be explained by the increase in lattice vibrations with temperature.
As temperature increases, the lattice vibrations disrupt the motion of charge carriers, increasing resistivity.
The relationship between resistivity and temperature is given by the equation:
- $\rho = \rho_0(1 + \alpha(T - T_0))$
- Where $\rho_0$ is the resistivity at a reference temperature $T_0$, and $\alpha$ is the temperature coefficient of resistivity.

Slide 3: Temperature Coefficient of Resistivity

The temperature coefficient of resistivity, $\alpha$, expresses the change in resistivity per unit change in temperature.
It is given by the equation:
- $\alpha = \frac{1}{\rho}\frac{d\rho}{dT}$
The temperature coefficient can be positive or negative, depending on the material.
For most metals, the temperature coefficient is positive, indicating an increase in resistivity with temperature.
For some materials like semi-conductors, the temperature coefficient can be negative, indicating a decrease in resistivity with temperature.

Slide 4: Current and Electricity

Electric current is the flow of electric charge through a conductor.
It is measured in amperes (A), and the symbol for current is I.
Electric current can be represented as the rate of flow of charge:
- $I = \frac{Q}{t}$
- Where Q is the charge flowing through a conductor in time t.
In a circuit, current flows from the positive terminal of a battery to the negative terminal.

Slide 5: Deviation from Ohm’s Law

Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across it, for a constant temperature.
Mathematically, Ohm’s Law can be written as:
- $V = I \cdot R$
- Where V is the voltage, I is the current, and R is the resistance.
However, not all materials obey Ohm’s Law. Some materials exhibit non-linear current-voltage characteristics.

Slide 6: Non-ohmic Conductors

Materials that do not follow Ohm’s Law are called non-ohmic conductors.
Non-ohmic conductors have a current-voltage relationship that is not linear.
Examples of non-ohmic conductors include diodes and transistors.
These materials have specific current-voltage characteristics determined by their physical properties and the operating conditions.

Slide 7: Resistivity and Resistance

Resistance ($R$) is a measure of the opposition to current flow in a conductor.
It is given by the equation:
- $R = \frac{\rho \cdot L}{A}$
- Where $\rho$ is resistivity, L is the length of the conductor, and A is its cross-sectional area.
Resistivity is a material property, while resistance depends on the dimensions of the conductor.

Slide 8: Conductors, Insulators, and Semi-conductors

Materials can be classified into three categories based on their electrical conductivity:
1. Conductors: Materials that allow the easy flow of electric charge.
2. Insulators: Materials that impede the flow of electric charge.
3. Semi-conductors: Materials that have intermediate electrical conductivity.
The conductivity of a material depends on its atomic and molecular structure.

Slide 9: Examples of Conductors, Insulators, and Semi-conductors

Examples of conductors include copper, silver, gold, and aluminum.
These materials have high conductivity due to the presence of loosely bound electrons in their atomic structure.
Examples of insulators include rubber, glass, and plastic.
Insulators have a large band gap, which prevents the flow of charge.
Examples of semi-conductors include silicon and germanium.
These materials have a small band gap, allowing for some flow of charge at certain temperatures.

Slide 10: Superconductivity

Superconductivity is a phenomenon observed in certain materials at very low temperatures.
Superconductors have zero electrical resistance below a critical temperature.
When a superconductor is cooled below its critical temperature, it can conduct electric current indefinitely without any loss of energy.
Superconducting materials have a wide range of practical applications, such as in MRI machines and particle accelerators.

Slide 11: Electric Power

Electric power is the rate at which electrical energy is consumed or produced.
It is measured in watts (W), and the symbol for power is P.
Electric power can be calculated using the equation:
- $P = I \cdot V$
- Where P is power, I is current, and V is voltage.
The unit of power is equivalent to one joule per second.

Slide 12: Kirchhoff’s Laws

Kirchhoff’s laws are fundamental principles used to analyze electrical circuits.
Kirchhoff’s first law, also known as the law of conservation of charge, states that the sum of the currents entering a junction is equal to the sum of the currents leaving the junction.
Kirchhoff’s second law, also known as the voltage law, states that the sum of the potential differences around any closed loop in a circuit is zero.
These laws are essential for solving complex circuits and understanding the behavior of current and voltage in circuits.

Slide 13: Series and Parallel Circuits

In a series circuit, components are connected one after another, so the same current flows through each component.
The total resistance of a series circuit is the sum of the resistances of individual components.
In a parallel circuit, components are connected in branches, so the voltage across each component is the same, but the current splits between the branches.
The total resistance of a parallel circuit can be calculated using the formula:
- $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$

Slide 14: Capacitors

A capacitor is an electronic component that stores and releases electrical energy.
It consists of two conductive plates separated by a dielectric material.
When a voltage is applied across the plates, positive charge accumulates on one plate and negative charge on the other.
The amount of charge stored by a capacitor is proportional to the voltage across it and is given by the equation:
- $Q = C \cdot V$
- Where Q is the charge, C is the capacitance, and V is the voltage.

Slide 15: Time Constant in RC Circuits

In an RC circuit, which consists of a resistor (R) and a capacitor (C), the time constant ($\tau$) is the time it takes for the voltage across the capacitor to reach approximately 63% of its final value.
The time constant is given by the equation:
- $\tau = R \cdot C$
- It represents the time required for the capacitor to charge or discharge to a particular level.
The time constant is an important parameter in determining the transient behavior of RC circuits.

Slide 16: Inductors

An inductor is an electronic component that stores energy in a magnetic field.
It consists of a coil of wire wound around a core.
When a current flows through an inductor, a magnetic field is created, and energy is stored in this field.
The amount of energy stored in an inductor is proportional to the square of the current and the inductance (L) of the inductor.

Slide 17: Self-Induction

Self-induction is a phenomenon in which changing current in a coil induces a voltage in the same coil.
This induced voltage opposes the change in current, according to Faraday’s law of electromagnetic induction.
Self-inductance is a property of a coil that determines the amount of voltage induced per unit change in current.
The unit of self-inductance is the henry (H).

Slide 18: Mutual Induction

Mutual induction is a phenomenon in which the changing current in one coil induces a voltage in another nearby coil.
This is the basis for the operation of transformers.
The mutual inductance (M) between two coils is a property that determines the amount of voltage induced in one coil per unit change in current in the other coil.
Mutual inductance is also measured in henries (H).

Slide 19: Transformers

A transformer is a device that transfers electrical energy between two or more coils through electromagnetic induction.
It consists of a primary coil and a secondary coil wound around a common core.
Transformers can step up or step down the voltage depending on the ratio of the number of turns in the primary and secondary coils.
The ratio of the voltage in the primary coil to the voltage in the secondary coil is equal to the ratio of the number of turns in the coils.

Slide 20: Electrical Safety

Electrical safety is essential to prevent electrical shocks, fires, and other accidents.
Some safety measures to follow include:
- Never touch electrical appliances with wet hands.
- Keep electrical cords away from heat sources and water.
- Use properly grounded outlets and surge protectors.
- Ensure that electrical circuits are not overloaded.
- Use circuit breakers or fuses to protect circuits from excessive current.

Slide 21: Magnetic Fields and Forces

A magnetic field is a region in which a magnetic force can be detected.
It is produced by moving charges, such as electrons in a current-carrying wire.
Magnetic field lines indicate the direction of the magnetic field and are represented by arrows.
The direction of a magnetic field is given by the “right-hand rule”: if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field.
Charged particles moving in a magnetic field experience a magnetic force given by the equation:
- $F = q \cdot v \cdot B \cdot \sin(\theta)$
- Where F is the magnetic force, q is the charge, v is the velocity, B is the magnetic field, and $\theta$ is the angle between the velocity and the magnetic field.

Slide 22: Applications of Magnetic Fields

Magnetic fields have various practical applications, including:
1. Electric motors: Use the interaction of magnetic fields and electric currents to generate rotational motion.
2. Transformers: Use mutual induction to transfer electrical energy between different voltage levels.
3. Magnetic resonance imaging (MRI): Uses strong magnetic fields and radio waves to create detailed images of the body’s internal structures.
4. Maglev trains: Use magnetic levitation to suspend and propel trains without any physical contact between the train and the track.
5. Cathode ray tube (CRT): Uses magnetic deflection to control the movement of the electron beam in televisions and monitors.

Slide 23: Faraday’s Law of Electromagnetic Induction

Faraday’s law of electromagnetic induction explains how a changing magnetic field induces an electromotive force (emf) in a conductor.
It states that the emf induced in a loop of wire is proportional to the rate of change of the magnetic flux through the loop.
The magnetic flux through a loop is given by the equation:
- $\Phi = B \cdot A \cdot \cos(\theta)$
- Where $\Phi$ is the magnetic flux, B is the magnetic field, A is the area of the loop, and $\theta$ is the angle between the magnetic field and the normal to the loop.
Mathematically, Faraday’s law is written as:
- $emf = -\frac{d\Phi}{dt}$
- The negative sign indicates that the induced emf creates a current that opposes the change in magnetic flux.

Slide 24: Lenz’s Law

Lenz’s law is a consequence of Faraday’s law and states that the direction of the induced current in a conductor is such that it opposes the change causing it.
This law is based on the principle of conservation of energy.
The induced current generates a magnetic field that opposes the original change in flux.
For example, if a magnetic field through a loop of wire is decreasing, the induced current will flow in a direction that creates a magnetic field opposing the decrease.
Lenz’s law plays a crucial role in understanding the behavior of induced currents in various applications.

Slide 25: Electromagnetic Waves

Electromagnetic waves are transverse waves that consist of oscillating electric and magnetic fields.
They can travel through a vacuum or a medium.
Electromagnetic waves include a wide range of frequencies, from radio waves, microwaves, and infrared radiation to visible light, ultraviolet radiation, X-rays, and gamma rays.
The speed of electromagnetic waves in a vacuum is a fundamental constant, approximately equal to the speed of light (3.00 x 10^8 m/s).
Electromagnetic waves transfer energy without requiring a medium for their propagation.

Slide 26: Characteristics of Electromagnetic Waves

Electromagnetic waves have several characteristics, including:
1. Wavelength (λ): The distance between two consecutive crests or troughs of the wave.
2. Frequency (f): The number of complete oscillations of the wave per unit time.
3. Amplitude (A): The maximum displacement of the wave from its equilibrium position.
4. Period (T): The time taken for one complete oscillation of the wave.
5. Velocity (v): The speed at which the wave propagates through a medium or vacuum.

Slide 27: Electromagnetic Spectrum

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic waves.
It includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.
Each region of the electromagnetic spectrum has different properties and applications.
Radio waves are used for communication, microwaves for cooking and communication, visible light enables us to see, and X-rays are used for medical imaging.
The energy and frequency of electromagnetic waves increase from radio waves to gamma rays.

Slide 28: Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material when it is exposed to electromagnetic radiation, usually in the form of light.
The energy of the light is transferred to the electrons, causing them to overcome the binding forces and escape from the material.
The photoelectric effect cannot be explained by wave theory alone and requires the particle-like nature of light (photons).
The energy of a photon is given by the equation:
- $E = hf$
- Where E is the energy of the photon, h is Planck’s constant (6.63 x 10^-34 J·s), and f is the frequency of the radiation.
The photoelectric effect played a crucial role in the development of quantum mechanics.

Slide 29: Dual Nature of Light

The dual nature of light refers to its ability to exhibit both wave-like and particle-like properties.
This concept is encapsulated in the principle of wave-particle duality.
In certain experiments, light behaves as a wave, such as interference and diffraction.
In other experiments, light behaves as a particle, such as the photoelectric effect and the Compton scattering of photons.
The wave-particle duality is a fundamental aspect of quantum physics and has revolutionized our understanding of the nature of light and matter.

Slide 30: Quantum Mechanics

Quantum mechanics is a branch of physics that deals with the behavior of matter and energy at the smallest scales.
It describes the properties and interactions of particles at the atomic and subatomic levels.
Quantum mechanics provides a mathematical framework for understanding phenomena such as the wave-particle duality, the quantization of energy levels in atoms, and the probabilistic nature of observing physical quantities.
It has led to the development of many modern technologies, such as transistors, lasers, and quantum computers.
Quantum mechanics is a complex and abstract theory, but it is essential for explaining the behavior of the microscopic world.