Lecture A Fundamentals and Background

Charge “Charge” is the basic quantity in electrical circuit analysis Fundamental charge quantity is the charge of a single electron Charge will be in integer multiples of a single electron’s charge Units of charge = Coulombs (C) One Coulomb  -6.2  electrons

Electric Fields A charge induces an electric field (E-field) The electric field is a vector field Point charge E- field:

Analogy: E-field vs. Gravitational field Electric Field: Gravitational Field:

Forces on Charged Particles A second “charge” placed in the electric field induces a force on both charges Coulomb’s Law: Electric field is essentially the force per unit charge placed in the field “Like” charges repel; opposite charges attract

Analogy: Mass in a Gravitational Field Coulomb’s Law: Newton’s Law:

Demo: static electricity charge on balloon causes it to stick to wall

Energy Transfer In circuit analysis, we are primarily concerned with energy transfer Charges move around Moving a charge in an electric field changes the charge’s potential energy Work to move charge from b to a:

Electric Potential Difference  W ba is the work required to move a charge from point b to point a in an electric field Work is a form of energy   W ba is a difference in potential energy (units are Joules, J) This difference is typically quantified as an Electric Potential Energy Difference Electric potential difference is the electrical potential energy difference per unit charge:

Voltage  V ba is generally referred to as a voltage difference; (units of  V ba are volts, V) Generally defined in terms of derivatives, for infinitesimal variations in charge and energy:

Notes on Voltage The potential energy difference is due to a physical separation (a distance) between the two points This potential difference provides a force which can move charges from place to place. This is sometimes called an electromotive force (emf)

Charge in motion & current Recall : We are concerned with energy transfer  charge motion emf (or potential energy difference, or voltage difference) can move charges Current is the time rate of change of charge

Charge Motion in Materials Common model of materials: Materials composed of atoms Atoms contain protons and neutrons in a nucleus, surrounded by a “cloud” of electrons Protons are positively charged, and are bound “tightly” in the nucleus Electrons are negatively charged, and bound less “tightly” to the atom

Charge Motion in Materials -- continued Electrons can move from atom to atom within a material. We can transfer charge through a material via electron motion Current is defined as the motion of “positive” charge Positive current is (by definition) in opposite direction to electron flow

Charge motion in materials -- continued We apply a potential difference across the material emf causes electron motion away from negatively charged end Current is in the direction of “positive” charge motion

Current Flow in Materials The less “tightly” bonded the electrons are to the atom, the more “easily” the material allows current to flow The material conducts electricity more easily The material has less resistance or higher conductivity For example, conductors have low resistance to current flow  low potential differences can provide high currents insulators have high resistance to current flow  nearly no current flow, even with high potential differences

Demo: touch electric fence with conductor and insulator

General Passive Circuit Elements General, two-terminal, passive circuit element Apply a voltage difference across the terminals This voltage difference results in current flow Our circuit elements will be electrically neutral Current entering the element is the same as the current leaving the element

Power Power is the rate of change of energy with time Units of power are Watts (W)

Power Generation and Dissipation Power dissipation: Current enters the positive voltage terminal Examples: Power dissipated as heat (light bulbs) Power converted to mechanical system (electric motors, pumps) Power generation Current enters the negative voltage terminal Examples: Power generated by mechanical system (turbines, generators) Power generated by chemical processes (batteries)

Demos? – Pulling mass across surface with DC motor (point out energy added, dissipated) – Pump water through horizontal tubing (point out energy exchange)