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 ↓


Electric circuits


Electrical circuits are one of the fundamental building blocks in the study of electromagnetism and electrical engineering. Understanding electrical circuits is essential to developing a strong understanding of how electricity can be used to power our homes, appliances, and technologies. This comprehensive explanation aims to outline the basic concepts, components, and principles that underlie electrical circuits in a simple manner.

What is an electrical circuit?

An electrical circuit is a closed loop or pathway that allows electric charge to flow. It typically includes a power source, various electrical components such as batteries, resistors, capacitors, and inductors, and the wires or traces on a circuit board that connect them. The flow of electrical charge is called electric current, and this current is driven by the potential difference or voltage supplied by the power source.

Basic components of an electrical circuit

  • Power source: The power source, such as a battery or generator, provides the electro-power (emf) needed to push electrons through the circuit.
  • Conductor: Wire or strands made of conductive materials, such as copper, that carry electric charges through a circuit.
  • Load: Devices or components that use electricity, such as lights, motors, or speakers. They convert electrical energy into other forms of energy.
  • Switch: A device that can open or close a circuit, allowing or stopping the flow of electricity.
  • Resistors: Components that resist the flow of electric current, used to control the current flow in a circuit.

Ohm's law

One of the fundamental principles governing electrical circuits is Ohm's Law. Ohm's Law presents the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit.

V = I * R

Where:

  • V is the voltage in the circuit in volts (V).
  • I is the current flowing in the circuit in amperes (A).
  • R is the resistance of the circuit in ohms (Ω).

Ohm's law shows that for a constant resistance, the current flowing through a circuit is directly proportional to the voltage applied across it. This law helps in analyzing circuits and designing them to work effectively.

Visual example: Ohm's law

V R I

In the above visual example, a simple circuit is shown with voltage (V), current (I), and resistance (R) in series connections.

Types of electrical circuits

Electrical circuits can be constructed in different configurations, based on how the components are connected. The two primary types are series circuits and parallel circuits.

Series circuit

In a series circuit, the components are connected end-to-end in a single path for the current to follow. If any part of the circuit breaks, the entire circuit stops working. The total resistance in a series circuit is the sum of the individual resistances:

Rtotal = R1 + R2 + R3 + ...

The voltage across the entire series circuit is the sum of the voltages across each component, and the current flowing through each component is the same.

Visual example: Series circuit

This figure shows a series circuit with two resistors connected one after the other.

Parallel circuit

In parallel circuits, components are connected at the same two points, providing multiple paths for current to flow. Unlike series circuits, if one path is broken, current can still flow through the other paths. The inverse of the total resistance in a parallel circuit is the sum of the inverses of the individual resistances:

1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...

In a parallel circuit, the voltage across each component is the same, while the total current is the sum of the currents through each path.

Visual example: Parallel circuit

This diagram shows a parallel circuit with resistors connected at two points, causing the current flow to diverge.

Complex circuits

Complex circuits involve a combination of both series and parallel connections. Analyzing such circuits often requires breaking them down into simpler parts and applying Ohm's Law and the laws of series and parallel circuits.

Kirchhoff's laws

For more complex circuits, we use Kirchhoff's circuit laws, which are two rules about the behavior of currents and voltages around a closed circuit loop.

Kirchhoff's current law (KCL)

Kirchhoff's current law states that the total current entering a junction or node is equal to the total current leaving that node.

ΣIin = ΣIout

This law reflects the conservation of charge, stating that what goes in must come out.

Kirchhoff's voltage law (KVL)

Kirchhoff's voltage law states that the sum of the electric potential differences (voltages) around a closed loop or mesh in a circuit is zero.

ΣV = 0

This principle represents conservation of energy, and ensures that all energy supplied to a circuit is used by the components within the loop.

Applications of electrical circuits

Electric circuits pave the way for a wide range of applications that are fundamental parts of modern technology. The effects of electric circuits span across a variety of applications, from simple light bulb circuits to complex motherboards in computers.

Lighting circuit

The most common application of electrical circuits is in lighting systems where the circuits are used to power light bulbs. Both series and parallel configurations are adopted to wire these systems depending on the desired outcome in terms of reliability and control.

Signal processing

Electronic circuits are fundamental to signal processing, which is used in radio, television, and mobile communications. Circuits in these devices amplify, modulate, and process signals for effective communication.

Power supply systems

Electrical circuits are used in power supply systems to ensure proper distribution and regulation of electrical power in various sectors and industries. These circuits need to be efficient to minimise energy loss during transmission.

Common problems and solutions

When working with electric circuits, several common problems may be encountered, such as short circuits, open circuits, and incorrect connections. Learning how to troubleshoot these problems is important for maintaining and repairing circuits.

Short circuit

A short circuit occurs when a low-resistance path allows excessive current to flow, potentially damaging components and creating a fire hazard. Short circuits can be caused by faulty connections or damaged wiring. Solutions include inspecting the connections and replacing faulty parts.

Open circuit

An open circuit occurs when the flow of current through a broken path stops, causing the circuit to not function. This can be caused by a broken connection or the failure of a component. Identifying and repairing broken connections or replacing failed components will restore functionality.

Incorrect connection

Incorrect connections can cause components to be incorrectly integrated into a circuit, causing unexpected behavior or damage. Checking the circuit layout against the schematics ensures correctness in connections.

Conclusion

The study of electrical circuits is a fundamental aspect of physics and engineering, providing critical understanding and skills to advance technology and electrical applications. From simple components like resistors and capacitors to complex circuit design and analysis using Ohm's and Kirchhoff's laws, mastering electrical circuits opens the door to countless innovative applications and advancements. Through continued exploration and practical application, the principles of electrical circuits will continue to drive our world forward.


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Electric circuits

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