Alexander Ch 02 Final r 1
Transcript of Alexander Ch 02 Final r 1
-
7/24/2019 Alexander Ch 02 Final r 1
1/16
1
Alexander-SadikuAlexander-SadikuFundamentals of Electric CircuitsFundamentals of Electric Circuits
Chapter 2Chapter 2
Basic LawsBasic Laws
Copyright The McGraw-Hill Companies, Inc. Permission require !or reprouction or isplay.
-
7/24/2019 Alexander Ch 02 Final r 1
2/16
2
"asic #aws - Chapter $"asic #aws - Chapter $
$.1 %hm&s #aw.
$.$ 'oes, "ranches, an #oops.
$.( )irchho!!&s #aws.
$.* +eries esistors an oltage i/ision.
$.0 Parallel esistors an Current i/ision.
$. 2ye-elta Trans!ormations.
-
7/24/2019 Alexander Ch 02 Final r 1
3/16
3
$.1 %hms #aw 314$.1 %hms #aw 314
5 %hm&s law states that the /oltage acrossa resistor is irectly proportional to thecurrent I !lowing through the resistor.
5 Mathematical e6pression !or %hm&s #awis as !ollows7
5 Two e6treme possi8le /alues o! 70 (ero! and (infinite! are relate
with two 8asic circuit concepts7 shortcircuitan open circuit.
iRv =
-
7/24/2019 Alexander Ch 02 Final r 1
4/16
4
$.1 %hms #aw 3$4$.1 %hms #aw 3$4
5 Conductance is the a8ility o! an element toconuct electric current9 it is the reciprocal o!resistance an is measure in mhos orsiemens.
5 The power issipate 8y a resistor7
v
i
RG ==
1
R
vRivip
2
2===
-
7/24/2019 Alexander Ch 02 Final r 1
5/16
5
$.$ 'oes, "ranches an #oops$.$ 'oes, "ranches an #oops314314
5 : 8ranchrepresents a single element such as a/oltage source or a resistor.
5 : noeis the point o! connection 8etween twoor more 8ranches.
5 : loopis any close path in a circuit.
5 : networ; with 8 8ranches, n noes, an l
inepenent loops will satis!y the !unamentaltheorem o! networ; topology7
1+= nlb
-
7/24/2019 Alexander Ch 02 Final r 1
6/16
6
$.$ 'oes, "ranches an #oops$.$ 'oes, "ranches an #oops3$43$4
Example "
#ow man$ %ranches& nodes and loops are there'
%riginal circuit
-
7/24/2019 Alexander Ch 02 Final r 1
7/16
7
$.$ 'oes, "ranches an #oops$.$ 'oes, "ranches an #oops3(43(4
Example 2
#ow man$ %ranches& nodes and loops are there'
Should we consider it as one%ranch or two %ranches'
-
7/24/2019 Alexander Ch 02 Final r 1
8/16
8
$.($.( )irchho!!&s #aws 314)irchho!!&s #aws 314
5 )irchho!!&s current law 3)C#4 states that thealge8raic sum o! currents entering a noe3or a close 8ounary4 is =ero.
0
1
==
N
n
niMathematically,
-
7/24/2019 Alexander Ch 02 Final r 1
9/16
9
$.($.( )irchho!!&s #aws 3$4)irchho!!&s #aws 3$4Example
5 etermine the current I !or the circuit shown inthe !igure 8elow.
) * -(-+!-2 , 0
) , -A
.his indicates thatthe actual currentfor ) is flowin/
in the oppositedirection2e can consier the whole
enclose area as one >noe?.
-
7/24/2019 Alexander Ch 02 Final r 1
10/16
10
$.($.( )irchho!!&s #aws 3(4)irchho!!&s #aws 3(4
5 )irchho!!&s /oltage law 3)#4 states that thealge8raic sum o! all /oltages aroun a close path
3or loop4 is =ero.
Mathematically, 01
==
M
m
nv
-
7/24/2019 Alexander Ch 02 Final r 1
11/16
11
$.($.( )irchho!!&s #aws 3*4)irchho!!&s #aws 3*4
Example
5 :pplying the )# equation !or the circuit o! the!igure 8elow.
va-v1-vb-v2-v3 = 0
V1 = IR1 v2 = IR2 v3 = IR3
va-vb = I(R1 + R2 + R3)
321 RRR
vvI ba
++
=
-
7/24/2019 Alexander Ch 02 Final r 1
12/16
12
$.* +eries esistors an oltage$.* +eries esistors an oltagei/ision 314i/ision 314
5 +eries7 Two or more elements are in series i! theyare cascae or connecte sequentially
an consequently carry the same current.
5 The equi/alent resistance o! any num8er o!resistors connecte in a series is the sum o! theini/iual resistances.
5 The /oltage i/ier can 8e e6presse as==+++=
N
nnNeq RRRRR
1
21
vRRR
Rv
N
nn
+++
=
21
-
7/24/2019 Alexander Ch 02 Final r 1
13/16
13
Example +
"01 and are in series
$.* +eries esistors an oltage$.* +eries esistors an oltagei/ision 314i/ision 314
-
7/24/2019 Alexander Ch 02 Final r 1
14/16
14
$.0 Parallel esistors an Current$.0 Parallel esistors an Currenti/ision 314i/ision 314
5 Parallel7 Two or more elements are in parallel i!they are connecte to the same two noes anconsequently ha/e the same /oltage across them.
5 The equi/alent resistance o! a circuit with' resistors in parallel is7
5 The total current i is share 8y the resistors inin/erse proportion to their resistances. The currenti/ier can 8e e6presse as7
Neq RRRR
1111
21
+++=
n
eq
n
nR
iR
R
vi ==
-
7/24/2019 Alexander Ch 02 Final r 1
15/16
15
Example
2& + and 2Aare in parallel
$.0 Parallel esistors an Current$.0 Parallel esistors an Currenti/ision 314i/ision 314
-
7/24/2019 Alexander Ch 02 Final r 1
16/16
16
$. 2ye-elta Trans!ormations$. 2ye-elta Trans!ormations
)(1
cba
cb
RRR
RRR
++
=
)(2
cba
ac
RRR
RRR
++=
)(3
cba
ba
RRR
RRR
++
=
1
133221
R
RRRRRRRa
++=
2
133221
R
RRRRRR
Rb++
=
3
133221
R
RRRRRRRc
++=
elta -3 Star Star -3 elta