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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.

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"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.

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$.1 %hms #aw 314$.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 =

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$.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===

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$.$ '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

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$.$ 'oes, "ranches an #oops$.$ 'oes, "ranches an #oops3$43$4

Example "

#ow man$ %ranches& nodes and loops are there'

%riginal circuit

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$.$ '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'

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$.($.( )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,

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$.($.( )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?.

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$.($.( )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

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$.($.( )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

++

=

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$.* +eries esistors an oltage$.* +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

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Example +

"01 and are in series

$.* +eries esistors an oltage$.* +eries esistors an oltagei/ision 314i/ision 314

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$.0 Parallel esistors an Current$.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 ==

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Example

2& + and 2Aare in parallel

$.0 Parallel esistors an Current$.0 Parallel esistors an Currenti/ision 314i/ision 314

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$. 2ye-elta Trans!ormations$. 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