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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)
Defined in terms of ampereMeasured in coulomb (C) = As
t
tidttqtq
0
')()( 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).
General, simple circuit element– two terminals– cannot be decomposed further– completely characterized by its
voltage-current relationship
Pushing charge– expenditure of energy– electrical voltage (potential difference)– voltage "across" the element
Basics - Voltage
A general two-terminalcircuit element
Voltage measures workrequired to move chargeRepresenting voltage– numerical value (+ unit) (e.g., -2.5 V)– direction (sense) ( + V - )
(left terminal is V volts positive withrespect to the right terminal)
– unit is volt (V = J / C)– represented by V, v, v(t)
Basics - Voltage
A general two-terminalcircuit element
Symbols: (a) DC voltage source;(b) battery; (c) ac voltage source.
Power is the rate of energyexpenditure: Voltage * Current– Voltage defined in terms of energy– Current is rate at which charge moves
Representing power– 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 - Power
A general two-terminalcircuit element
Is a choice we make (convention)The current arrow is directedinto the "+" marked terminalThe power absorbed by the elementis given by the product p = v iA negative value indicates that poweris actually generatedOr: The power generated by theelement is given by the product p = - v i
Basics - Passive sign convention (PSC)
A general two-terminalcircuit element, p = vi represents the power absorbed
Resistance of conducting elementOhm's law: v = R i– linear, directly proportional
Passive elementPower p = v i = i2 R = v2 / RRepresenting resistance– numerical value (+ unit) (e.g., 3 )– unit is ohm ( = V / A)– represented by R
Basics - Resistor
NodesBranchesPathsLoops
Circuits
(a) A circuit containing three nodes and five branches.
(b) Node 1 is redrawn to look like two nodes; it is still one node.
Kirchhoff's current law
Conservation of charge
Circuits - KCL
The algebraic sum of the currentsentering any node is zero.
iA + iB - iC - iD = 0
Kirchhoff's voltage law
Conservation of energy
Circuits - KVL
The algebraic sum of the voltagesaround any closed path is zero.
v1 = v2 - v3
2
1 3
A B
C
+
-
+ -
-
+
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 - SourcesExamples 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.
An illustration of voltage division.
vRR
Rv
21
22
For a string of N series resistors ....
vRRR
Rv
N
kk
...21
Current division
Using KCL and Ohm's law to find i2.
iRR
Ri
21
12
For a parallel combination of N resistors
the current through Rk equals ....
i
RRR
Ri
N
kk 1
...11
1
21
An illustration of
current division.
Simplifying circuits (KVL)
V a+--
V b-+
R 1
v1
+ --
V c
V a+--
V b--+
R 1
+ --
V c
V 1+--
R 1
V 2--+
R 1
K VL
K VL
V1 = Va - Vb + Vc
V2 = -Va + Vb - Vc
• What do we count as positive?
• Direction of summation determines polarity
1st choice
2nd choice