Physical Sciences 3 Final: Lecture 4a

• School: Harvard University
• Department: Physical Sciences
• Course: Physical Sciences 3
• Professor: Roxanne Guenette

Document Summary

A circuit with a resistor and capacitor in series is an rc circuit. The current through the capacitor is the time derivative of its charge: i = dq dt . If the capacitor is charged, you can discharge it through the resistor: The time constant rc is the time required for the charge to drop to 37% of its initial value. If the capacitor is uncharged, you can charge it with a battery: Q(t ) = qmax 1 e t rc. We can model the membrane as a network of resistors and capacitors. This network acts like a bunch of rc circuits in which one circuit charges the next, and so on down the membrane. As a result, an electrical signal can propagate passively down the membrane. To describe signal propagation, we need to consider the membrane potential as a function of position. This leads to the following simplified expression for the propagation of a potential spike: