Download Mesh Current Method, Lecture Set 5

ECE 3336
Introduction to Circuits & Electronics
Note Set #1
Voltage, Current, Energy and Power
Spring 2015,
TUE&TH 5:30-7:00 pm
Dr. Wanda Wosik
1
Introduction to EE
• Basic concepts in circuits:
– Current
Analogy to Hydraulic Systems
– Voltage
– Polarities (reference and actual)
2
3
4
Charge
proton: + charge
electron: - charge
Here the atom is
negatively charged
1C=Q(6.2414 x1018) electrons
1 proton: q = 1[C]/ 6.2414 x1018 = 1.6022 x10 -19 [C]
1 electron: q = -1.6022 x 10 -19 [C]
Atomic number of atom = # protons or electrons / atom
The energy acquired by an electron when accelerated
by 1.0 V is 1.0 eV.
1.0 eV = 1.60221x10-19 C * 1.0 V=1.60221x10-19 J
5
Example
How many Cu atoms have -1 [C] of electrons?
Atomic
number
1 atom:
qe ==2929(-1.6022 x10-19 ) [C]
so
1[C]
# atoms 
29 1.6022 1019 [C/atom]

or

# atoms  2.1522 1017
6
Current
Current is the rate of flow of charge
water analogy:
Hydraulic analogy
Water flow in the pipe
pipe with water
++++
current flows from left to right
wire with current
Convention: current flows in the direction of positive charge
motion (established by Benjamin Franklin).
7
Current
In reality, the electrons are the charges that move in a wire.
Ions do not move
Convention: electrons moving in one direction is equivalent
to positive charges moving in the other direction.
++++
8
Current [unit]
• [Ampere] = 1 [Coulomb] of charge moving per [second]
1[A] = 1[Coul/sec]
• The number of charges per second flowing for each Ampere
of current is called a Coulomb, which is about 6.24 x 1018
electron charges.
1C/1.6022 x10 -19[C]
+ Charges flowing
is equivalent to
- Charges flowing in the opposite direction
++++
1 [A]
flow rate = 1 [C/s]
9
Current: Formal Definition
• Current is the net flow of charges, per time, past an arbitrary “plane” in
an electrical device (the simplest will be a resistor).
• We will only be concerned with the flow of positive charges.
• A negative charge moving to the right is conceptually the same as a
positive charge moving to the left.
• In conductors electrons=negative charges flow and constitute current.
• Mathematically, current is expressed as…
Current,
typically in
Amperes [A]
dq
i=
dt
Charge, typically in
Coulombs [C]
Time, typically in
seconds [s]
10
Current (cont.)
In fact + charges can also flow ≈ current flows
In semiconductors, both electrons (-) and holes (+) are the
charges that move: diodes, transistors, some resistors.
In electrochemistry + ions flow  ionic current: metal
electroplating, fluidics, plasma etc.
www.saskschools.ca/curr_content/chem30_05/6_redox/r
edox2_2.htm
11
Definition of Current
Current I is a flow of charge.
• If the flow is constant, charge does not change q/t and it lasts
some time (t), we can find relation
q[C] = I[A]t[s]
• In the case of “alternating current” ac, there is instantaneous
charge change and we have
dq[C]
i[A] =
dt[s]
Area
-
+
All electrons (it is a conductor) flow - +
with drift velocity v
Change of charge in unit time
carrier density n – this varies with materials
dN – total # of charges passing the area A
d(qN)
I=
= nq • v • A
dt
d(qN) = dq• N + q• dN
d(qN) = qdN = q(vdt • A)n
12
Hydraulic Analogy for Current
• More intuitive analogy: current flow is analogous to the water flow.
Animated graphic provided by David Warne, student in UH ECE Dept.
13
Illustration: Water flow and Current
• Water flow rate is determined by the volume of water moving (measured
at inserted plane) in a second
• Current is the number of positive charges moving in a second (measured
also at such plane).
Animated graphic provided by David Warne, student in UH ECE Dept.
14
Voltage
Potential energy describes the capacity to do work ex. E=mgh
(gravitation) will change to kinetic energy E=mv2/2.
Electric potential energy U: refers to a charge q moved in an
electric field E generated by another charge Q. Charge will
experience force F.
From Coulomb Law:
Voltage
Equipotential
lines
F kQq kQ
E = = 2 = 2 [V /m]
q qr
r
kQq
q F = 2 = qE
r
Voltage=Work done per unit charge
dW F × ds
=
= E × ds
q
q
Voltage ~ to energy (U) loss/gain
V = E×d
Ex. q=1C, VAB=1V
Energy gain/loss 1Joule
k=1/40
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html
kQq
U=
[eV ]
r
V[V ] =
U[eV ]
q[e]
15
Voltage: Formal Definition
• When we move a charge in the presence of other
charges, energy is transferred.
• Voltage corresponds to the change in potential energy
as we move between two points; it is a potential
difference.
Voltage,
typically in
Volts [V]
dw
v=
dq
Energy, typically in
Joules [J] (or in eV)
Charge, typically in
Coulombs [C]
(or expressed as e)
16
Voltage [unit]
• Unit: Volt.
• Volt is defined as Joule per Coulomb
• Verify units: V=J/C
• Remember that voltage is defined in terms of the
energy gained or lost by the movement of positive
charges.
ex. 1V=1J/1C
17
Hydraulic Analogy With Two Paths
Like height, voltage
is path independent.
Water is flowing
through the pipes
(analogy to
current).
The height
between two
points does
not change
as you go
through the
two pipes.
The height difference
for water
• Pressure
Potential difference
• Voltage
Height
18
Hydraulic Analogy:
Voltage and Current
height ~ voltage
flow rate ~ current
19
Hydraulic Analogy:
Voltage and Current
20
The Battery
A Source of Voltage.
Physical Appearance.
Nigel P. Cook
Electronics: A Complete Course, 2e
Schematic Symbol.
Copyright ©2004 by Pearson Education, Inc.
21 07458
Upper Saddle River, New Jersey
All rights reserved.
Using the Voltmeter to Measure Voltage.
Nigel P. Cook
Electronics: A Complete Course, 2e
Copyright ©2004 by Pearson Education, Inc.
22
Upper Saddle River, New Jersey 07458
All rights reserved.
Polarities
Polarity refers to
• Directions of currents
• Signs of voltages
It is extremely important to know the polarity of the
voltages and currents in circuits.
Use:
• Reference polarities i.e. assumed (chosen)
direction for the purposes of keeping track
• Actual polarities i.e. real current and voltage
directions calculated from a circuit.
23
Polarities for Currents
• For current, the reference polarity is given by an arrow.
• The actual polarity is indicated by a value that is associated with
that arrow.
• In the diagram below, the currents i1 and i2 are not defined until
the arrows are shown.
i2
i1
-3 Amps 3 Amps
a wire
i1 = 3 Amps
i2 = -3 Amps
These are all different ways to show the same thing, a
current of 3 Coulombs per second of positive charges
moving from left to right through this wire.
The arrow shows a reference polarity, and the sign of the
number that goes with that arrow shows the actual
polarity.
24
Polarities for Voltages
• For voltage, the reference polarity is given by a + symbol and a –
symbol, at or near the two points involved.
• The actual polarity is indicated by a value that is placed between the +
and - symbols.
Device
+
-
+
-
v1(t)
v2(t)
5V
-5V
-
+
-
+
25
Energy and Power
• Basic concepts: energy and power
• Sign Conventions for power direction
– Energy /power can be delivered or absorbed
• Hydraulic analogy to energy and power helps to
visualize electricity
26
Energy
• It is the ability to do work.
• Energy can have many forms: heat, light,
sound, motion etc.
Unit is Joule or [J]
1 [Joule]=[Newton•meter].
In everything that we do in circuit analysis, energy will
be conserved.
Circuit elements can absorb or deliver energy.
27
Power
• Power is the rate of change of the energy, with time. It is the rate
at which the energy is absorbed or delivered.
• Power can be absorbed or delivered.
• Units: Watts or [W].
Defined as a [Joule per second] W=J/s
• Light bulbs are rated in [W]. Thus, a 100 [W] light bulb is one that
absorbs 100 [J] every second that it is turned on.
Power,
typically in
Watts [W]
dw
p=
dt
Energy, typically in
Joules [J]
Time, typically in
seconds [s]
28
Power from Voltage and Current
• Power can be found from the voltage and current.
•
Note that if voltage is given in [V], and current in [A], power will come
out in [W].
dw dw dq
p=
=
´
= vi
dt dq dt
Verify units: W=J/s=J/C•C/s=V•A
29
Sign Conventions or Polarity Conventions
•
Sign conventions, or polarity conventions determine whether power
and energy are delivered or absorbed
•
A sign convention is a relationship between reference polarities for
voltage and current.
•
As in all reference polarity issues, you can’t choose reference
polarities wrong.
30
Passive Sign Convention – Definition
•
The passive sign convention is when the reference polarity for
the current is in the direction of the reference voltage drop
i.e. current enters the positive terminal for the reference
polarity for the voltage.
•
Passive Sign Convention
iX
Circuit
Circuit
+
-
vX
vY
-
+
iY
31
Passive Sign Convention (examples)
•
The circuits shown have reference polarities which are
in the passive sign convention.
•
They look different, but the circuits have the same
relationship between the polarities of the voltage and
current.
Passive Sign Convention
iX
Circuit
Circuit
+
-
vX
vY
-
+
iY
32
Active Sign Convention
•
The active sign convention is when the reference polarity for the current is
in the direction of the reference voltage rise.
•
Same as current entering the negative terminal for the reference polarity
for the voltage.
Active Sign Convention
iW
Circuit
Circuit
-
+
vW
vZ
+
-
iZ
33
Using Sign Conventions for
Power Direction
•
The sign conventions will be used to determine
whether power is absorbed, or power is
delivered.
•
We might want to write an expression for power
absorbed by a device, circuit element, or other part
of a circuit. Use appropriate subscripts.
pabs ,device
34
Using Sign Conventions for
Power Direction
The sign conventions are used to determine whether power is
absorbed or delivered.
•
•
•
•
In passive sign convention:
(+) vi indicates the power absorbed
(-) vi indicates the power delivered.
In active sign convention:
•
•
(+) vi indicates the power delivered
(–) vi indicates the power absorbed.
Passive
Convention
Active
Convention
Power
absorbed
pABS = vi
pABS = -vi
Power
delivered
pDEL = -vi
pDEL = vi
35
Power Direction Table
Choice of
• Passive Convention (+ power for passive elements= power absorbed)
• Active Convention (+ power for active elements=power delivered)
Passive sign convention.
+
Sample
Circuit
is
vS
pabs = vsis
pdel = -vsis
iS
pabs = -vsis
pdel = vsis
Active sign convention.
Sample
Circuit
+
Power
absorbed
Power
delivered
Passive
Convention
Active
Convention
pABS = vi
pABS = -vi
pDEL = -vi
pDEL = vi
vS
iS
-
36
Passive
sign
gives
- power
The passive sign
convention used
here (a and b)
Generates
energy
Power (p=v • i):
pabs,B=-12 V•0.1 A=-1.2 W
pabs,1=8 V•0.1 A=0.8 W
pabs,2=4 V•0.1 A=0.4 W
The battery generates 1.2 W
Resistors absorb (0.8+0.4) W
So the energy is conserved
dissipated=
absorbed
generated=
Figure
delivered
2.22, 2.24
Passive
sign
gives
+ power
Dissipates
energy
Power (p=v • i):
pabs,B=-(-12 V)•(-0.1 A)=-1.2 W
pabs,1=-8 V•-0.1 A=0.8 W
pabs,2=-4 V•-0.1 A=0.4 W
We have the same results:
The battery generates 1.2 W
Resistors absorb (0.8+0.4) W
So the energy is conserved
37
Energy Conservation and
Conversion of Energy
In a typical lightning strike, 500 megajoules of electric potential energy are
converted into 500 megajoules (total) of light energy, sound energy, thermal
energy, and so on.
Chemical,
Thermal,
Electrical,
Mechanical,
Optical etc.
wikipedia.org
38
Energy and Power in Electrical Systems
•
Power delivered to the electrical system comes from other sources (ex.
other electrical systems, light sources, thermoelectric materials, chemical
battery etc.)
•
Since energy is conserved the power will be conserved as well.
Electrical System
made up of various parts
and components
Nonelectrical power
that will be converted
to electrical power
Component
in circuit
which
delivers
positive
power
Electrical power
that is delivered
to the system
39
Energy and Power in Electrical Systems
•
Power from the electrical system is absorbed by the “energy converter” and
results in delivery of new energy forms ex. mechanical (electrostriction), light
(LED, lasers), heat, chemical etc.
•
Again, since energy is conserved the power will be conserved as well.
Electrical System
made up of various parts
and components
Electrical power
that is absorbed
out of the system
Component
in circuit
which
absorbs
positive
power
Nonelectrical power
that was converted
from electrical power
40
DC Circuit Water Analogy
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html
41
DC Circuit Water Analogy
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html
42
Main Points
• Current[A]=flow of + charges
(or - in the opposite direction)
• Votage[V]=potential difference (=Efield/xdistance)
• Power[W]=vi
• conventions: passive and active define delivered and
absorbed power
• Power (and energy is conserved)
43