Transcript EE 221 Review 1

EE 221
Review 1
Basic components
Electric circuits
Voltage and current laws
Basics - SI base units
Base quantity
Name
Symbol
length
meter
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
temperature
kelvin
K
Basics - SI prefixes
Factor
Name Symbol Factor
Name Symbol
10-18
atto
a
10-15
femto
f
10-12
pico
p
1012
tera
T
10-9
nano
n
109
giga
G
10-6
micro

106
mega
M
10-3
milli
m
103
kilo
k
10-2
centi
c
Basics - Charge
Two types of charge
– positive: (proton)
– negative: (electron, -1.6 10-19C)
Continuously transferring charge
– total amount of charge never changed
– neither created nor destroyed (conservation)
t
Defined in terms of ampere q(t )  q(t0 )  t idt '
Measured in coulomb (C) = As
0
Basics - Current
Charge in motion
– transfer of energy
– related to charge
Representing current
–
–
–
–
numerical value (+ unit) (e.g., -13.5 A)
direction
(
)
unit is the ampere (A)
represented by I, i, i(t)
Symbol for an
independent current
source
Basics - Current
Example
(a,b) Incomplete, improper, and incorrect definitions of a current.
(c) the correct definition of i1(t).
Basics - Voltage
General, simple circuit element
– two terminals
– cannot be decomposed further
– completely characterized by its
voltage-current relationship
Pushing charge
A general two-terminal
circuit element
– expenditure of energy
– electrical voltage (potential difference)
– voltage "across" the element
Basics - Voltage
Voltage measures work
required to move charge
Representing voltage
– numerical value (+ unit) (e.g., -2.5 V)
– direction (sense)
(+ V -)
A general two-terminal
circuit element
(left terminal is V volts positive with
respect to the right terminal)
– unit is volt (V = J / C)
– represented by V, v, v(t)
Symbols: (a) DC voltage source;
(b) battery; (c) ac voltage source.
Basics - Power
Power is the rate of energy
expenditure: Voltage * Current
– Voltage defined in terms of energy
– Current is rate at which charge moves
Representing power
–
–
–
–
–
A general two-terminal
circuit element
numerical value (+ unit) (e.g., -5.6 W)
"direction" by Passive Sign Convention
PSC: Current entering element through positive terminal
unit is watt (W = V *A = J / C *A = J / (As) *A = J / s)
represented by P, p, p(t)
Basics - Passive sign convention (PSC)
Is a choice we make (convention)
The current arrow is directed
into the "+" marked terminal
The power absorbed by the element
is given by the product p = v i
A general two-terminal
circuit element, p = vi
A negative value indicates that power represents the power
absorbed
is actually generated
Or: The power generated by the
element is given by the product p = - v i
Basics - Resistor
Resistance of conducting element
Ohm's law: v = R i
– linear, directly proportional
Passive element
Power p = v i = i2 R = v2 / R
Representing resistance
– numerical value (+ unit) (e.g., 3 )
– unit is ohm ( = V / A)
– represented by R
Circuits
Nodes
Branches
Paths
Loops
(a) A circuit containing three
nodes and five branches.
(b) Node 1 is redrawn to look like
two nodes; it is still one node.
Circuits - KCL
Kirchhoff's
current law
Conservation
of charge
The algebraic sum of the currents
entering any node is zero.
iA + iB - iC - iD = 0
Circuits - KVL
v2
Kirchhoff's
voltage law
A
B
2
+
-
-
v3
3
1
v1
Conservation
of energy
-
+
C
+
The algebraic sum of the voltages
around any closed path is zero.
v1 = v2 - v3
Circuits - Sources
(a) Series connected voltage sources can be replaced by a
single source.
(b) Parallel current sources can be replaced by a single
source.
Circuits - Sources
Examples of circuits with multiple sources, some of
which are “illegal” as they violate Kirchhoff’s laws.
V-I Laws: Resistors
(a) Series combination of N resistors.
(b) Electrically equivalent circuit.
Req = R1 + R2 + ... + RN
V-I Laws: Resistors
(a) Parallel combination of N resistors.
(b) Electrically equivalent circuit.
1/Req = 1/R1 + 1/R2 + ... + 1/RN
A special case worth remembering is
Voltage division
Using KVL and Ohm's law to find v2.
v2 
R2
v
R1  R2
For a string of N series resistors ....
vk 
Rk
v
R1  R2  ...  RN
An illustration of
voltage division.
Current division
Using KCL and Ohm's law to find i2.
i2 
R1
i
R1  R2
For a parallel combination of N resistors
the current through Rk equals ....
ik 
1
Rk
1
1
1

 ... 
R1 R2
RN
An illustration of
current division.
i
Simplifying circuits (KVL)
R1
R1
Va
1st
choice
+
-KVL
+
--
• Direction of summation
determines polarity
V1 = Va - Vb + Vc
Vc
+
--
+
Vb
V1
• What do we count as
positive?
R1
2nd
choice
R1
Va
+
-KVL
Vb
-+
Vc
+
--
v1
V2
-+
V2 = -Va + Vb - Vc