Electric-circuit Simulation

Model and simulate current in an electric circuit.

← Differential Equations projects

Learn Mathematics Differential Equations

Question

How can a differential equation predict current and charge in an electric circuit?

Component values determine whether the circuit settles, oscillates, or resonates.
Component values determine whether the circuit settles, oscillates, or resonates.
A series circuit with an inductor, resistor, capacitor, and voltage source.
The RLC circuit used in the original engineering-mathematics material.

Goals

  • Build differential models for RL and RLC circuits.
  • Compare transient, damped, and resonant responses.

Method

Translate Kirchhoff's laws into equations for current or charge.

  • Combine the resistor, inductor, capacitor, and voltage terms in one model.
  • Solve the equation with Laplace transforms or a numerical method.
  • Change the components and input voltage, then graph the circuit response.

Try an example

Current Quest

Source code ↗ Open full screen ↗

Change the inductor, resistors, capacitor, and time interval. The Laplace-transform solution animates current around both loops and traces both current graphs.

Controls: Choose a response preset or enter component values, then select Apply & run. Use Space to pause, R to restart, or drag the time control.