Circuit Analysis I (ENGR 2405) - Houston Community College
Transcript of Circuit Analysis I (ENGR 2405) - Houston Community College
What is a circuit?
• An electric circuit is an interconnection of electrical
elements.
• It may consist of only two elements or many more:
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Units
• When taking
measurements, we must
use units to quantify
values
• We use the International
Systems of Units (SI for
short)
• Prefixes on SI units allow
for easy relationships
between large and small
values
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Electric Charge
When an amber rod is
rubbed with fur, some of
the electrons on the
atoms in the fur are
transferred to the amber:
Electric Charge:
Water (H2O) molecule can
be polarized by electrostatic
Induction For example, the
water molecule has more
positive charges on one side
of the molecule and negative
charges on the other side.
Thus, water can be slightly
attracted to a static electric
charge. A demonstration of
that can be seen in bending a
stream of water with a
charged plastic comb.
Electric Charge
Some materials can become
polarized – this means that their
atoms rotate in response to an
external charge. This is how a
charged object can attract a
neutral one.
Electric Charge
The electrons in an atom are in a cloud
surrounding the nucleus, and can be separated
from the atom with relative ease.
Electric Charge
We find that the total electric charge of the
universe is a constant:
Electric charge is conserved.
Also, electric charge is quantized in units of e.
The atom that has lost an electron is now
positively charged – it is a positive ion
The atom that has gained an electron is now
negatively charged – it is a negative ion
Many descriptions of electric charge use
terms that might lead you to the conclusion
that charge is a substance. Phrases like:
“Charge on a sphere”
“Charge transferred”
“Charge carried on the electron”
However, charge is a property of particles,
one of many properties, such as mass.
21.5 Charge is Quantized
Charge is Quantized
. Since the days of Benjamin Franklin, our understanding of
of the nature of electricity has changed from being a type of
‘continuous fluid’ to a collection of smaller charged particles.
The total charge was found to always be a multiple of a certain
elementary charge, “e”:
The value of this elementary charge is one of the fundamental
constants of nature, and it is the magnitude of the charge
of both the proton and the electron. The value of “e” is:
Charge is Quantized
Elementary particles either carry no charge, or carry a single
elementary charge. When a physical quantity such as charge
can have only discrete values, rather than any value, we say
the quantity is quantized. It is possible, For example, to find
a particle that has no charge at all, or a charge of +10e, or -6e,
but not a particle with a charge of, say, 3.57e.
Conductors and Insulators
Conductors are materials through which charge can move freely; examples include metals (such as
copper in common lamp wire), the human body, and tap water.
Nonconductors—also called insulators—are materials through which charge cannot move freely;
examples include rubber, plastic, glass, and chemically pure water.
Semiconductors are materials that are intermediate between conductors and insulators; examples
include silicon and germanium in computer chips.
Superconductors are materials that are perfect conductors, allowing charge to move without any
hindrance.
The properties of conductors and insulators are due to the structure and electrical nature of atoms.
Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral
neutrons. The protons and neutrons are packed tightly together in a central nucleus.
When atoms of a conductor come together to form the solid, some of their outermost (and so most
loosely held) electrons become free to wander about within the solid, leaving behind positively
charged atoms ( positive ions).We call the mobile electrons conduction electrons.
There are few (if any) free electrons in a nonconductor.
Charge
• Charge is a basic SI unit, measured in
Coulombs (C)
• Counts the number of electrons (or positive
charges) present.
• Charge of single electron is 1.602*10-19 C
• One Coulomb is quite large, 6.24*1018
electrons.
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Charge II
• In the lab, one typically sees (pC, nC, or
μC)
• Charge is always multiple of electron
charge
• Charge cannot be created or destroyed,
only transferred.
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Electric Current:
Although an electric current is a stream of moving charges, not all moving
charges constitute an electric current. If there is to be an electric current through
a given surface, there must be a net flow of charge through that surface. Two
examples are given.
1. The free electrons (conduction electrons) in an isolated length of copper wire
are in random motion at speeds of the order of 106 m/s. If you pass a
hypothetical plane through such a wire, conduction electrons pass through it in
both directions at the rate of many billions per second—but there is no net
transport of charge and thus no current through the wire. However, if you
connect the ends of the wire to a battery, you slightly bias the flow in one
direction, with the result that there now is a net transport of charge and thus an
electric current through the wire.
The figure shows a section of a conductor, part of a conducting loop in which current has been
established. If charge dq passes through a hypothetical plane (such as aa’) in time dt, then the current i
through that plane is defined as:
The charge that passes through the plane in a time interval extending from 0 to t is:
Under steady-state conditions, the current is the same for planes aa’, bb’, and cc’ and for all planes that
pass completely through the conductor, no matter what their location or orientation.
The SI unit for current is the coulomb per second, or the ampere (A):
Electric Current:
Current
• The movement of charge is called a current
• Historically the moving charges were
thought to be positive
• Thus we always note the direction of the
equivalent positive charges, even if the
moving charges are negative.
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Current II
• Current, i, is measured as charge
moved per unit time through an
element.
• Unit is Ampere (A), is one
Coulomb/second
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dt
dqi
DC vs. AC
• A current that remains constant
with time is called Direct Current
(DC)
• Such current is represented by the
capital I, time varying current uses
the lowercase, i.
• A common source of DC is a
battery.
• A current that varies sinusoidally
with time is called Alternating
Current (AC)
• Mains power is an example of AC
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Direction of current
• The sign of the current indicates the
direction in which the charge is
moving with reference to the direction
of interest we define.
• We need not use the direction that the
charge moves in as our reference, and
often have no choice in the matter.
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Direction of Current II
• A positive current through a
component is the same as a negative
current flowing in the opposite
direction.
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Electric Potential:
The potential energy per unit charge at a point in an electric field is called the electric
potential V (or simply the potential) at that point. This is a scalar quantity. Thus,
The electric potential difference V between any two points i and f in an electric field is equal
to the difference in potential energy per unit charge between the two points. Thus,
The potential difference between two points is thus the negative of the work done by the
electrostatic force to move a unit charge from one point to the other.
If we set Ui =0 at infinity as our reference potential energy, then the electric potential V must
also be zero there. Therefore, the electric potential at any point in an electric field can be
defined to be
Here W∞ is the work done by the electric field on a charged particle as that particle
moves in from infinity to point f.
The SI unit for potential is the joule per coulomb. This combination is called the volt
(abbreviated V).
Voltage
• Electrons move when there is a
difference in charge between two
locations.
• This difference is expressed at the
potential difference, or voltage (V).
• It is always expressed with reference to
two locations
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Voltage II
• It is equal to the energy needed to
move a unit charge between the
locations.
• Positive charge moving from a higher
potential to a lower yields energy.
• Moving from negative to positive
requires energy.
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Power in Electric Circuits:
In the figure, there is an external conducting path between
the two terminals of the battery. A steady current i is
produced in the circuit, directed from terminal a to
terminal b. The amount of charge dq that moves between
those terminals in time interval dt is equal to i dt.
This charge dq moves through a decrease in potential of
magnitude V, and thus its electric potential energy
decreases in magnitude by the amount
The power P associated with that transfer is the rate of
transfer dU/dt, given by
The unit of power is the volt-ampere (V A).
Energy and Power in Electric Circuits
When the electric company sends you a bill,
your usage is quoted in kilowatt-hours (kWh).
They are charging you for energy use, and kWh
are a measure of energy.
Power and Energy
• Voltage alone does not equal power.
• It requires the movement of charge, i.e. a
current.
• Power is the product of voltage and current
• It is equal to the rate of energy provided or
consumed per unit time.
• It is measured in Watts (W)
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vip
Passive Sign Convention
• By convention, we say that
an element being supplied
power has positive power.
• A power source, such as a
battery has negative power.
• Passive sign convention is
satisfied if the direction of
current is selected such that
current enters through the
terminal that is more
positively biased.
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Conservation of Energy
• In a circuit, energy cannot be created or
destroyed.
• Thus power also must be conserved
• The sum of all power supplied must be
absorbed by the other elements.
• Energy can be described as watts x
time.
• Power companies usually measure
energy in watt-hours
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Circuit Elements
• Two types:
– Active
– Passive
• Active elements can
generate energy
– Generators
– Batteries
– Operational Amplifiers
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Circuit Elements II
• Passives absorb energy
– Resistors
– Capacitors
– Inductors
• But it should be noted that only the
resistor dissipates energy ideally.
• The inductor and capacitor do not.
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Ideal Voltage Source
• An ideal voltage source has no internal
resistance.
• It also is capable of producing any
amount of current needed to establish
the desired voltage at its terminals.
• Thus we can know the voltage at its
terminals, but we don’t know in
advance the current.
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Ideal Current Source
• Current sources are the opposite of the
voltage source:
• They have infinite resistance
• They will generate any voltage to
establish the desired current through
them.
• We can know the current through them
in advance, but not the voltage.
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Ideal sources
• Both the voltage and current source
ideally can generate infinite power.
• They are also capable of absorbing
power from the circuit.
• It is important to remember that these
sources do have limits in reality:
• Voltage sources have an upper current
limit.
• Current sources have an upper voltage
limit. 38
Dependent Sources
• A dependent source has its output
controlled by an input value.
• Symbolically represented as a
diamond
• Four types:
– A voltage-controlled voltage source
(VCVS).
– A current-controlled voltage source
(CCVS).
– A voltage-controlled current source
(VCCS).
– A current-controlled current source
(CCCS).
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Dependent Source example
• The circuit shown below is an example
of using a dependent source.
• The source on the right is controlled by
the current passing through element C.
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Circuit Applications of
Dependent Sources • Dependent sources are good models
for some common circuit elements: – Transistors: In certain modes of operation,
transistors take either a voltage or current input
to one terminal and cause a current that is
somehow proportional to the input to appear at
two other terminals.
– Operational Amplifiers: Not covered yet, but the
basic concept is they take an input voltage and
generate an output voltage that is proportional to
that.
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