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
electrons -6.2
10 18
Electric Fields
• A charge induces an
electric field (E-field)
• The electric field is a vector
field
• Point charge E- field:
E
q R
2
Analogy: E-field vs. Gravitational field
•
Electric Field:
•
Gravitational Field:
E
q R
2
m R
2
Forces on Charged Particles
• A second “charge” placed in the
electric field induces a force on both charges
• Coulomb’s Law:
F
q
1
q
2
R
2
q
2
E
• 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:
F
q
1
q
2
R
2
q
2
E
F
m
1
m
2
R
2
m
2
• 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:
W ba
a
b
F
d s
q a
b
E
d s
•
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:
V ba
W ba q
•
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:
v
dw dq
change in energy change in charge
Joules Coulomb
Volts , V
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
i
dq dt
change in charge change in time
Coulombs
A mperes Second , A
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
potential differences can provide high currents
• insulators have high resistance to current flow
current flow, even with high potential differences low nearly no
• 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
P
dW dt
dW dq
dq dt
v
i
• 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)