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:

2R

qR̂E

Analogy: E-field vs. Gravitational field

• Electric Field: • Gravitational Field:

2R

qR̂E

2R

mR̂

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

EqR

qqF

22

21

Analogy: Mass in a Gravitational Field

• Coulomb’s Law: • Newton’s Law:

EqR

qqF

22

21

2221 m

R

mmR̂F

• 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

a

b

a

ba sdEqsdFW

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:

q

WV ba

ba

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:

dq

dwv

charge in change

energy in change V ,Volts

Coulomb

Joules

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

dt

dqi

time in change

charge in change A ,mperesA

Second

Coulombs

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)

ivdt

dq

dq

dW

dt

dWP

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)