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9/6/2005
1
Welcome to ENEE 204
Welcome to ENEE 204
Basic Circuit Theory
Basic Circuit Theory
Lecture 3
Lecture 3
TOPICS:
9/6/2005
2
Formulas of the
Instantaneous
Power
Consumption of Various Devices
Resistor:
iR
v
=
)
(
)
(
)
(
t
i
t
v
t
p
=
R
v
R
p
2
2
i
=
=
Capacitor:
dt
dv
C
i
=
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
=
2
2
Cv
dt
d
dt
dv
v
C
p
Always positive: always
consumes energy
If power > 0 : absorbs energy
If power < 0 : gives energy
Inductor:
dt
di
L
v
=
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
=
2
2
Li
dt
d
dt
di
i
L
p
If power > 0 : absorbs energy
If power < 0 : gives energy
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9/6/2005
3
Circuit Analysis
Circuit Analysis
Goal:
to figure out the CURRENTS,
I’s and VOLTAGES, V’s in ALL
circuit elements.
v
s
=20V
i
s
R
2
=5
Ω
i
2
,
v
2
i
1
,
v
1
R
1
=5
i
A
=2 A
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CHAPTER 2: KCL and KVL
CHAPTER 2: KCL and KVL
•
Rules to obtain the voltages and currents in all
parts of the circuit
I
S
I
1,,
v
1
I
3,,
v
3
I
2,,
v
2
I
4,,
v
4
I
5,,
v
5
I
6,,
v
6
I
7,,
v
7
I
8,,
v
8
•
i
k
: current through
element, k
•
v
k
: voltage acrosss
element, k
3
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Terms Used in Analyzing Circuits
Terms Used in Analyzing Circuits
1. Branch
– any line with one 2terminal device
2. Node
 point at which branches meet (
)
(a point where two or more elements are
connected together)
trivial node: only two elements are connected
nontrivial node: more than two are joined
3. Loop

set of branches that form a closed path (
)
4. Mesh
 the simplest type of loop ( no element is inside the loop)
trivial mesh: contains only 2 elements
nontrivial mesh: more than 2 elements
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A
loop
loop
is a set of branches that form a
closed path.
Here are some example loops
Each node is encountered only once as the loop is traced.
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9/6/2005
7
A
mesh
mesh
is the simplest type of
loop
loop
.
*
Meshes do not enclose any branches
Here are some examples
of nontrivial meshes.
Here is an example of
a trivial mesh.
* For a planar circuits only
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Example: Identifying nodes and neshes
Branches: 14
NODES:
Nontrivial
(6) and
trivial
nodes (3)
Note: BE CAREFUL OF OVER COUNTING NODES!
(connecting lines are assumed to have no resistances)
NOT
NODES !
MESHES:
Nontrivial
(4) and
trivial
meshes (2)
5
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Kirchhoff’s
Kirchhoff’s
Current Law (KCL)
Current Law (KCL)
Kirchhoff's
Kirchhoff's
Voltage Law (KVL)
Voltage Law (KVL)
i
1
(t)
i
2
(t)
i
3
(t)
i
4
(t)
i
5
(t)
∑
i
k
(t) = 0
k
KCL: The
algebraic
algebraic
sum of electric
currents
at any
node
is equal to
zero at every instant of time.
+
sign: current is going
into
the node

sign: current is going
out
of the node
0
5
4
3
2
1
=
−
−
+
−
i
i
i
i
i
KVL: The
algebraic
sum of the voltages at any
loop
is
equal to zero at every instant of time.
v
2
(t)
v
s
(t)
Loop trace
v
6
(t)
v
1
(t)
v
3
(t)
∑
v
k
(t) = 0
k
+
sign:
tracing direction
is going
into
the + terminal
sign:
tracing direction
is going
into
the – terminal
Signs of terminal are determined by
REF. DIRECTIONS
.
0
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This note was uploaded on 04/07/2008 for the course ENEE 204 taught by Professor Gomez during the Fall '04 term at Maryland.
 Fall '04
 Gomez

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