2012/9/17 1 Basic Laws •Ohm’s Law(resistors) • Nodes, Branches, and Loops •Kirchhoff’s Laws • Series Resistors and Voltage Division • Parallel Resistors and Current Division • Wye-Delta Transformations • Applications Ohm’s Law • Resistance R is represented by •Ohm’s Law: A R R v + _ i 1 = 1 V/A Cross-section area A Meterial resistivity ohm R i v
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Basic Laws [相容模式] - National Chiao Tung University · Basic Laws •Ohm’s Law (resistors) •Nodes, Branches, and Loops •Kirchhoff’s Laws •Series Resistors and Voltage
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2012/9/17
1
Basic Laws
•Ohm’s Law (resistors)•Nodes, Branches, and Loops•Kirchhoff’s Laws•Series Resistors and Voltage Division•Parallel Resistors and Current Division•Wye-Delta Transformations•Applications
Ohm’s Law•Resistance R is represented by
•Ohm’s Law:
AR
Rv+
_
i
1 = 1 V/A
Cross-sectionarea A
Meterialresistivity
ohm
Riv
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Resistors
0Riv == R = 0v = 0
+
_
i
R = v
+
_
i = 0
0Rv
limiR
==∞→
Variable resistor Potentiometer (pot)
Open circuitShort circuit
Nonlinear Resistors
i
v
Slope = R
v
i
Slope = R(i) or R(v)
Linear resistor Nonlinear resistor
•Examples: lightbulb, diodes•All practical resistors may exhibit certain
nonlinear behavior.
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Conductance and PowerDissipation
•Conductance G is represented by
vi
RG
11 S = 1 = 1 A/V
siemens mho
Gi
Gvivp
Rv
Riivp
vGi
22
22
===
===
=
positive R : power absorption (+)
negative R: power generation (-)
Nodes, Branches, & Loops•Branch: a single element (R,
C, L, v, i)
•Node: a point of connectionbetween branches (a, b, c)
•Loop: a closed path in acircuit (abca, bcb, etc)–An independent loop contains
at least one branch which isnot included in other indep.loops.
–Independent loops result inindependent sets of equations.
+_
a
c
b
+_
c
ba
redrawn
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ContinuedElements in parallelElements in series
•Elements in series–(10V, 5)
• Elements in parallel–(2, 3, 2A)
•Neither–((5/10V), (2/3/2A))
10V
5
2 3 2A+_
Kirchhoff’s Laws•Introduced in 1847 by German physicist G. R.
Kirchhoff (1824-1887).
•Based on conversation of charge and energy.
•Two laws are included,Kirchhoff’s current law (KCL) andKirchhoff’s votage law (KVL).
•Combined withOhm’s law, we have apowerful set of tools for analyzing resistivecircuits.
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KCL
i1i2
in
0211
nn
N
niiii
•Assumptions–The law of conservation of charge–The algebraic sum of charges within a system
cannot change.
•Statement–The algebraic sum of currents entering a node
(or a closed boundary) is zero.
Proof of KCL
proved)(KCLanyfor0)()(
anyfor0)(it.onstoredbetoallowednotisCharge
object.physicalanotisnodeA
)()(
)()(1
ttidt
tdqttq
dttitq
titi
TT
T
TT
n
N
nT
i1i2
in
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Example 1
i1
i3i2
i4
i5
leaving,entering,
52431
54321 0)-()-(
TT
T
ii
iiiii
iiiiii
Example 2
321
312
IIII
IIII
T
T
I1 I2 I3
ITIT
321 IIIIS
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Case with A Closed Boundary
cancelled.arecurrentsbranchInternal
0
0
0
1111
baab
nbn
mam
jbj
iai
iiii
ii
ii
a
Treat the surfaceas a big node
leavingentering ii
b
ia1
ib1
KVL
01
m
M
mv
•Assumption–The principle of conservation of energy
•Statement–The algebraic sum of all voltage drops (or rises)