Overview

Electricity powers the world. Circuit theory is the language of electronics. It explains how to route electrons to do useful work, from lighting a bulb to processing information.

Core Idea

Ohm’s Law: $V = IR$. Voltage (Pressure) = Current (Flow) $\times$ Resistance (Restriction). This simple equation is the foundation of everything.

Formal Definition (if applicable)

Kirchhoff’s Laws:

  1. KCL (Current Law): What goes in must come out (Conservation of Charge).
  2. KVL (Voltage Law): The sum of voltage drops in a loop is zero (Conservation of Energy).

Intuition

Water Analogy:

  • Voltage: Water pressure (pump).
  • Current: Water flow rate (gallons per minute).
  • Resistance: Narrow pipe.
  • Capacitor: Water tank (storage).
  • Inductor: Heavy water wheel (inertia).

Examples

  • Series Circuit: Old Christmas lights (one goes out, they all go out).
  • Parallel Circuit: House wiring (one light goes out, the rest stay on).
  • AC vs. DC: AC (Alternating Current) for power grid; DC (Direct Current) for batteries/electronics.

Common Misconceptions

  • “Electrons move fast.” (They actually move very slowly—drift velocity. The energy wave moves at the speed of light.)
  • “Batteries store charge.” (They store chemical energy.)
  • Power: $P = VI$ (Watts).
  • Impedance: Resistance in AC circuits (includes frequency effects).
  • Semiconductors: Diodes and Transistors (electronic switches).

Applications

  • Electronics: Phones, computers, TVs.
  • Power Systems: Grid distribution.
  • Automotive: Electric vehicles.

Criticism / Limitations

Ideal circuit models ignore real-world effects like parasitic resistance and electromagnetic interference (EMI).

Further Reading

  • Horowitz & Hill, The Art of Electronics
  • Nilsson & Riedel, Electric Circuits