Circuits and dynamics

How can two resistors turn a 12 V supply into an 8 V signal? Why does connecting a load change that signal? Where does the electrical energy go? And what changes when a component can store energy?

Start here even if circuits are your first Eqiora topic. We build the equations from charge and energy balance, make a prediction on paper, and express the same relations in .eqi. After running the complete model, we replace its component definitions with a standard import. You can then recognize exactly which physics the shorter program contains.

Follow the circuit

Chapter	Question you will answer
1. Voltage, current, and power	How can a source have negative absorbed power?
2. Conserving networks	What do a wire, a junction, and ground each assert?
3. Build and run a divider	Can the equations predict 4 mA, 8 V, and the complete power balance?
4. Open the components	When can we reuse a resistor, and when must its law change?
5. Storage and decay	How does storing charge introduce a state and a time scale?

The first two chapters need algebra and unit conversions. Chapter 5 introduces the derivative as a rate of change and works through the required exponential solution. Each chapter includes exercises and answer sketches; no other book is a prerequisite.

The first calculation

For a 12 V ideal source and series resistors of 1 kΩ and 2 kΩ, the same current passes through both:

$$I=\frac{12\,\mathrm{V}}{3\,\mathrm{k\Omega}}=4\,\mathrm{mA}, \qquad V_{\mathrm{out}}=I(2\,\mathrm{k\Omega})=8\,\mathrm{V}.$$

This small example gives us a complete scientific loop: a physical assumption, a derivation, a calculation, and a way to discover that an assumption no longer fits. A loaded divider, for example, needs a different junction equation even though each resistor still obeys the same law.

For computation, use the environment from Get started. Keep its eqiora-source checkout and .venv; the run instructions below use those names. You can also read all derivations and work the exercises without installing anything.

Follow the energy into another subject

A resistor’s electrical loss is heat generation. Continue into heat transfer to ask where that heat flows and how temperature changes. For the distinction between a physical law and a solver, visit mathematical modeling; for errors in a computed time history, visit numerical simulation.

Begin: Voltage, current, and power · Explore another subject