Simulation of Charges in Simple Circuits

Click on each picture to see the relaxation of the circuits to their steady-state configuration. The papers (below) have more refined pictures.

A few improved calculations, taking account the propagation delay of the electric field, are now available.

I have written two papers about these calculations: A is an unpublished paper which discusses the surface charges and feedback mechanisms in these simple circuits, and is pedagogically oriented. B is a more high-powered paper published by the American Journal of Physics, 68, 1002-1006 (2000), and discusses the electric fields, equipotentials, and Poynting vectors in these circuits.
Simple RC circuit image The simplest resistor-capacitor circuit studied: a capacitor and a uniform resistive wire. The colors show the amount of excess charge in each cell, and the arrows show the direction and magnitude of the electric field. In steady-state, the electric field has the same magnitude everywhere to create the same current at all points in the circuit.
Resistive wire image This wire has an extra resistor: a higher impedance region made of a different material. The electric field must be larger in the high-resistive region (and smaller in the low-resistance wires) to have uniform current.
Narrow wire image This wire has an extra resistor: a higher impedance region formed by narrowing the wire. The electric field must be larger in the high-resistive region (and smaller in the low-resistance wires) to have uniform current.
Sinuous wire image This wire has extra bends, requiring a more complex arrangement of surface charges to have the same current everywhere in the circuit.

Norris Preyer