Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Electromagnetism → Electromagnetic induction ↓


Transformers and Inductive Circuits


In electromagnetic induction, the transformer is one of the most important applications. A transformer is a device that uses the principles of electromagnetic induction to transform electrical energy from one circuit to another. This involves changing voltage levels, which makes it indispensable in electrical systems, especially in power distribution.

Basic principles of transformers

Transformers work on the principle of mutual induction. When alternating current flows through a primary coil, it produces a changing magnetic field. This magnetic field, in turn, induces an electromotive force (EMF) in the secondary coil placed near it. The voltage induced in the secondary coil can be determined by the equation:

V_s / V_p = N_s / N_p

Where:

  • V_s = voltage in the secondary coil
  • V_p = voltage in the primary coil
  • N_s = number of turns in the secondary coil
  • N_p = number of turns in the primary coil

This equation shows that the voltage is directly proportional to the number of turns. If the secondary coil has more turns than the primary coil, the transformer is a step-up transformer. Conversely, if the secondary coil has fewer turns, it is a step-down transformer.

Visualization of transformers

Primary Coil Secondary coil main

This diagram shows the basic setup of a transformer. The blue lines represent the coils, while the red line represents the shared core made of ferromagnetic material. This core transmits the magnetic field created by the primary coil to the secondary coil.

Inductive circuits and their components

Inductive circuits are circuits that include inductors as a main component. An inductor is a passive two-terminal electrical component that stores energy in a magnetic field. The formula for inductance, which deals with how effectively energy is stored, is:

V = L * (di/dt)

Where:

  • V is the voltage across the inductor
  • L is the inductance, measured in henry (H)
  • (di/dt) is the rate of change of current through the inductor

Visualizing a simple inductor circuit

l

This simplified diagram shows the symbol for an inductor in a circuit, which is characterized by loops representing the inductive properties. Inductors resist changes in current, which makes them important for managing energy transfer in a circuit.

Applications and examples

Transformers and inductive circuits are used in many applications:

  • Power Grid: Transformers are important in power grids to step up voltage for long distance transmission and to minimise energy losses.
  • Electronics: Inductors are used in a variety of electronic devices to filter signals, store energy, or manage electric current.
  • Motors: Transformers and inductive circuits are integral to the operation of electric motors and other machines that convert electrical energy into mechanical energy.

Understanding transformer efficiency

Transformer efficiency is the ratio of output power to input power, usually expressed as a percentage:

Efficiency (%) = (P_out / P_in) * 100

Because of energy losses such as resistance and magnetic leakage in the coils, no transformer is 100% efficient. Optimizing these processes is essential in designing an effective transformer.

Visualization of efficiency in transformers

input power Electricity generation

The green rectangle represents the input power, while the red rectangle represents the output power. The difference between the two represents the losses, which shows why efficiency is important in transformer functionality.

Advanced concepts in transformers

In addition to the basic step-up and step-down transformers, there are several advanced concepts:

  • Autotransformers: These transformers use a single coil, which acts as both the primary and secondary winding, and has variable tapping points.
  • Three-phase transformers: These transformers, used in large-scale power systems, are configured to work with three alternating currents simultaneously.
  • Isolation Transformer: Designed to electrically isolate primary and secondary circuits, useful for safety and noise reduction in sensitive equipment.

Conclusion

Transformers and inductive circuits are the backbone of modern power systems, important in both small electronics and large-scale power networks. Understanding their operation, efficiency, and applications is helpful in understanding both fundamental and advanced aspects of electromagnetism.


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Transformers and Inductive Circuits

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