Electrical Engineering

The fundamental relationship stating that the voltage across a conductor is directly proportional to the current flowing through it, expressed as $V = IR$. This law is the cornerstone of circuit analysis and is used to predict how electrical components behave under different conditions.

Two circuit analysis principles: Kirchhoff's Current Law (KCL) states that all currents entering a node must sum to zero, and Kirchhoff's Voltage Law (KVL) states that all voltages around any closed loop must sum to zero. Together they enable systematic analysis of complex circuits.

DC flows in one constant direction, as from a battery, while AC periodically reverses direction, as in household power outlets. AC is preferred for long-distance power transmission because transformers can easily step its voltage up or down, minimizing energy loss.

The generalization of resistance to AC circuits, impedance accounts for both resistive and reactive (capacitive and inductive) opposition to current flow. It is expressed as a complex number with magnitude and phase angle, measured in ohms.

Semiconductors are materials whose electrical conductivity falls between conductors and insulators. By doping them with impurities to create p-type and n-type regions, engineers build diodes, transistors, and integrated circuits that form the basis of all modern electronics.

Discovered by Michael Faraday, this principle states that a changing magnetic field through a conductor induces an electromotive force (voltage). It is the operating principle behind electric generators, transformers, and induction motors.

The analysis, manipulation, and synthesis of signals such as audio, video, and sensor data. Techniques include filtering, Fourier transforms, modulation, and compression, applied in both analog and digital domains.

Control systems use feedback loops to maintain a desired output despite disturbances. A sensor measures the output, a controller compares it to the setpoint, and an actuator adjusts the system accordingly. Stability analysis ensures the system does not oscillate or diverge.

Power systems engineering deals with the generation, transmission, distribution, and utilization of electric power on a large scale. The grid must balance supply and demand in real time while maintaining stable frequency and voltage levels.

Digital logic uses binary states (0 and 1) implemented with transistor-based logic gates (AND, OR, NOT) to perform computation. Millions of these gates are combined in microprocessors that execute programmed instructions at billions of operations per second.