Transcript Slide 1
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 -6.21018 electrons Electric Fields • A charge induces an electric field (E-field) • The electric field is a vector field • Point charge E- field: q ˆ ER 2 R Analogy: E-field vs. Gravitational field • Electric Field: q ˆ ER 2 R • Gravitational Field: m ˆ R 2 R Forces on Charged Particles • A second “charge” placed in the electric field induces a force on both charges • Coulomb’s Law: q1 q 2 F 2 q2 E R • 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: q1 q 2 F 2 q2 E R • Newton’s Law: m1m2 ˆ F R 2 m2 R • 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: b Wba F ds q E ds b a a Electric Potential Difference • Wba is the work required to move a charge from point b to point a in an electric field • Work is a form of energy Wba 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: Wba Vba q Voltage • Vba is generally referred to as a voltage difference; (units of Vba are volts, V) • Generally defined in terms of derivatives, for infinitesimal variations in charge and energy: dw v dq change in energy Joules Volts , V Coulomb change in charge 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 dq i dt change in charge Coulombs Amperes , A Second change in tim e 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 dW dW dq P v i dt dq dt • 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)