Appendix A: Review of Basic Circuit Theory

Introduction

• Basic Electrical Parameters

  • Potential Difference (V or E)

  • Current (I)

  • Conductance (g)

  • Capacitance (C)

• Rules for Circuit Analysis

  • Conductance

  • Current

  • Capacitance

  • Potential Difference

• Current in Circuits with Capacitance

  • Circuit with Capacitor

  • Circuit with Resistor and Capacitor in Series

  • Circuit with Resistor and Capacitor in Parallel

Familiarity with the basic principles of electrical circuit theory is important for understanding the equivalent circuit model of the neuron developed in Chapters 6, 7, and 9. The appendix is divided into three parts:

1. The definition of basic electrical parameters.

2. A set of rules for elementary circuit analysis.

3. A description of current in circuits with capacitance.

Basic Electrical Parameters

Potential Difference (V or E)

Electrical charges exert an electrostatic force on other charges: like charges repel, opposite charges attract. The force decreases as the distance between two charges increases. Work is done when two charges that initially are separated are brought together. Negative work is done if their polarities are opposite and positive work if they are the same. The greater the values of the charges and the greater their initial separation, the greater the work done. (Work = where f is electrostatic force and r ₁ is the initial distance between the two charges.)

Potential difference is a measure of this work: The potential difference between two points is the work that must be done to move a unit of positive charge (one coulomb) from one point to the other (ie, it is the potential energy of the charge). One volt (V) is the energy required to move one coulomb a distance of one meter against a force of one newton.

Current (I)

A potential difference exists within a system whenever positive and negative charges are separated. Charge separation may be generated by a chemical reaction (as in a battery) or by diffusion of two electrolyte solutions with different ion concentrations across a selectively permeable barrier, such as a cell membrane. If a charge separation exists within a conducting medium, charges move between the areas of potential difference: Positive charges are attracted to the region with a more negative potential, and negative charges to the region of positive potential.

Current is defined as the net movement of charge per unit time. According to convention, the direction of current is defined as the direction of flow of positive charge. In metallic conductors current is carried by negatively charged electrons, which move in the opposite direction of conventionally defined current. In nerve and muscle cells current is carried by both positive and negative ions in solution. One ampere (A) of current represents the movement of one coulomb (of charge) per second.

Conductance (g)

Any object through ...