Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Electricity and Magnetism → Magnetism and Electromagnetism ↓


Inductance and Transformer


Inductance and transformers are fundamental concepts in the study of magnetism and electromagnetism. They form the backbone of many electronic devices and systems, including power grids, motors, inductors, and more. In this lesson, we will explore these concepts in detail using simple language, many examples, and visual illustrations.

Understanding induction

Inductance is a property of an electrical conductor that describes how strongly the conductor opposes a change in current. An inductor is a device, usually made of a coil of wire, that makes use of this property.

The main idea behind induction is Faraday's law of induction, which states that a change in magnetic flux through a circuit induces an electromotive force (EMF) in the circuit. Mathematically, it is expressed as:

EMF = -dΦ/dt

Where:

  • EMF is the electromotive force in volts.
  • Φ is the magnetic flux in webers (Wb).
  • t is the time in seconds.

Self priming

When current flows through a coil, it creates a magnetic field around it. If the current changes, the magnetic field also changes, which induces an EMF within the same coil. This phenomenon is known as self-induction.

The self-induced EMF is given by:

EMF = -L (di/dt)

Where:

  • L is the inductance of the coil in henry (H).
  • di/dt is the rate of change of current in amperes per second (A/s).

Example of self-motivation

Consider a simple coil with an inductance of 2 Henry. If the current flowing through the coil changes at the rate of 3 amperes per second, the induced EMF in the coil can be calculated as:

EMF = - 2 * 3 = -6 V

This means that an EMF of 6 volts is induced in the direction opposite to the change in current.

Mutual induction

Mutual induction occurs when a change in current in one coil induces an EMF in another nearby coil. This principle is the basis of transformers, where energy is transferred between two or more coils.

The mutual inductance between two coils can be expressed as:

EMF = -M (di/dt)

Where:

  • M is the mutual inductance between the coils, measured in henrys (H).
  • di/dt is the rate of change of current in the first coil.
Coil 1 Coil 2

In the above illustration, coil 1 carries a varying current which induces an EMF in coil 2 due to their mutual inductance.

Example of mutual induction

Suppose the mutual inductance of the two coils is 0.5 henry, and the current in the first coil changes at the rate of 4 amperes per second. The induced EMF in the second coil will be:

EMF = - 0.5 * 4 = -2 V

This means that an induced EMF of 2 volts is produced across coil 2.

Transformers

A transformer is a device that uses the principles of mutual induction to transfer energy between two circuits. A typical transformer has two coils: primary and secondary coils, which are wrapped around a magnetic core.

Working principle of transformer

When alternating current (AC) flows through the primary coil, it creates a changing magnetic field. This changing magnetic field then induces an electromotive force in the secondary coil according to Faraday's law.

Primary Coil Secondary coil

The figure shows a simple transformer with one primary and one secondary coil. The orange line shows the path of the magnetic field.

Transformer equations

The performance of a transformer is described by the relationship between the turns ratio of the primary and secondary coils and the voltage across them. The basic equation is:

Vp/Vs = Np/Ns

Where:

  • Vp is the voltage in the primary coil.
  • Vs is the voltage in the secondary coil.
  • Np is the number of turns in the primary coil.
  • Ns is the number of turns in the secondary coil.

The power in the transformer (neglecting losses) is given by:

Vp * Ip = Vs * Is

Where:

  • Ip is the current flowing in the primary coil.
  • There is current in the secondary coil.

Step-up and step-down transformers

Transformers can be classified into step-up and step-down depending on their turns ratio.

  • Step-up transformer: Increases the voltage from primary to secondary. It has fewer turns in the primary coil and more in the secondary (Np < Ns).
  • Step-down transformer: Reduces the voltage from primary to secondary. It has more turns in the primary coil and less in the secondary (Np > Ns).

Example of transformer calculation

Let us consider a transformer with a primary coil of 100 turns and a secondary coil of 200 turns. If the primary voltage is 120 volts, what is the secondary voltage?

Vp/Vs = Np/Ns
120/Vs = 100/200
Vs = 240 volts

This simple calculation shows that the transformer increases the voltage from 120 volts to 240 volts.

Applications of induction and transformer

Inductance and transformers are important in modern technology. Some applications include:

  • Electrical transmission: Transformers are used to step up and step down voltage in electrical grids, so that electric power can be efficiently transmitted over long distances.
  • Electronic devices: Inductors are used in tuning circuits to select desired frequencies, to smooth currents in power supplies, and in filters to block unwanted signals.
  • Motors and generators: Induction motors use induction to convert electrical energy into mechanical energy.

Conclusion

Induction and transformers play important roles in the field of electromagnetism, allowing the control and manipulation of electric currents and magnetic fields. Understanding these concepts enriches our knowledge of physics and provides practical tools for a variety of technological applications.


Grade 11 → 6.3.5


U
username
0%
completed in Grade 11

← Prev (6.3.4)
Faraday's and Lenz's laws
Next (6.3.6) →
Alternating current and its applications

Comments 



Inductance and Transformer

https://www.physicsflow.com/g11/6.3.5?pfal=en