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Electricity · Physics

DC circuits are bookkeeping for charge, energy, and power.

Learn the basic circuit elements, simplify networks using series/parallel combinations, and track energy transfer using power.

This topic

DC Circuits

Build circuit intuition: elements, combinations, equivalent resistance, and energy/power in steady-state circuits.

Elements
Circuit elements
DC circuits are built from sources and loads. The core model elements are idealized, but they are powerful for solving real problems.
  • Voltage sources and the meaning of emf
  • Resistors as energy-dissipating elements
  • Ideal wires: zero resistance, same node potential
  • Ground/reference node (choice of zero potential)
Start nano-lesson Circuits are about nodes and elements between nodes.
Simplify
Series and parallel combinations
Many networks can be simplified using series and parallel rules. The key is recognizing when components truly share the same current or the same voltage.
  • Series: same current through each element
  • Parallel: same voltage across each branch
  • Common mistakes: “looks parallel” vs “is parallel”
  • Using equivalent circuits to reduce complexity
Start nano-lesson Check node connections before applying formulas.
Tool
Equivalent resistance
Equivalent resistance replaces a network of resistors with a single resistor that draws the same current for a given applied voltage.
  • Compute Req by reduction (series/parallel)
  • Interpretation: same external V–I behavior
  • Sanity checks: Req bounds in series/parallel
  • Why equivalent circuits are physically meaningful
Start nano-lesson Always do a quick bounds check.
Energy
Energy and power in circuits
Circuits move energy from sources to loads. Power tells you how fast energy is transferred or dissipated.
  • Power in an element: P = IV
  • Resistors: P = I²R and P = V²/R
  • Energy over time: E = Pt for constant power
  • Qualitative efficiency and heating intuition
Start nano-lesson Power is where the “real-world cost” shows up.
Practice
Practice & Exercises
Practice reducing circuits, computing currents and voltages, and using power to interpret energy transfer.
  • Identify series vs parallel correctly from a diagram
  • Compute Req for multi-resistor networks
  • Find branch currents and element voltages in reduced circuits
  • Compute power and compare heating across components
  • Exam-style DC circuit reduction sets
Open practice sets Draw nodes clearly before you compute.