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@V__FD\ FNF@\_I@I\Y 3

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@V__FD\ FNF@\_I@I\Y

?.3 Fnf`tri` @urrfdt

_ctf be ebnbw be fnf`tri` hcrmf, PI Vdit is capcrf (C).

I 1t

q, whfrf 'q' is thf tbtcn `hcrmf cdl 't' is thf tiaf pfribl.

3 capfrf 1bdlsf`3

`bunbao3

3 capcrf is lfeidfl cs thf urrfdt id c wirf ie bdf bunbao be hcrmfs enbws thrbumh it id bdf sf`bdl.

?.? Lriet Ufnb`ity

Id `bdlu`tbrs, c ncrmf duaofr be erff fnf`trbds crf prfsfdt, whi`h abvf id rcdlba lirf`tibds. Ie

D0?3 u,.....u,u,urrrr

crf thfir rcdlba iditicn vfnb`itifs, thfd thf cvfrcmf thfracn vfnb`ity is

D

u,.....u,u,u D0?3rrrr

1 : .........(3)

E 1 fF

R+

R

CF

+

n

]hfd cd fxtfrdcn fnf`tri` eifnl Fr

is cppnifl c`rbss thf bdlu`tbr, thf fnf`trbds fxpfrifd`f c ebr`f,

E fF1r r

.........(?)

Ie afof thf acss be fnf`trbd, thfd thf c``fnfrctibd be fnf`trbd winn of,

faFfc

r

r -1 .........(0)

Vdlfr thf id ideunufd`f be fnf`tri eifnl, fnf`trbd abvf cdl suosfqufdtny bnnilf with thf tibds. \hf tiaf

oftwffd twb su` fssivf bnnisiubds is cnnfl _fncxctibd tiaf ( t ). hf vfnb`ity be fnf`ytrbd kust ofebrf

`bnnisibd is mivfd oy,

3vr

1 3ur

+ cr

3t .........(

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? @V__FD\ FNF@\_I@I\Y

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?.0 _fnctibd oftwffd Lriet Ufnb`ity cdl Fnf`tri` @urrfdt

Nft us bdsilfr thf bdlu`tbr be rbss sf`tibd crfc C cdl nfdmth n. \hfd thf vbnuaf be thf bdlu`tbr,

U 1 C n

Ie d of thf db. be erff fnf`trbds pfr udit vbnaf, thfd thf tbtcn hcrmf bd cnn thf erff fnf`trbds is mivfd oy,

q 1 d C nf .........(3)

Vdlfr thf idenufd`f be fnf`tri` eifnl, thf fnf`trbds winn trcvfn thf listcd`f nwith lriet vfnb`ity vlid

t 1lv

n

I 1t

q.........(?)

I 1 dfC vl

.........(0)

?.< Aboinity

\hf aboinity be erff fnf`trbds is lfeidfl cs thf lriet vfnb`ity c`quirfl pfr udit strfdmth be cppnifl fnf`tri`

eifnl. It is rfprfsfdtfl oy a. \hus,

lv

F

a 1

^ I 1 d C a F f

PI udit be aboinity a?U3s3

0. BHA'P NC]

\hf urrfdt thrbumh c bdlu`tbr is cnwcys lirf`tny prbpbrtibdcn tb thf p. l. c`rbss its twb fdls, suokf`t tb

pcrti`uncr physi cn bdlitibds (tfapfrcturf, prfssurf, ft`.) Acthfacti cnny.

I 1 U

Br wf cd scy thct, U 1 I

U 1 _I , whfrf _ is thf rfsistcd`f.

\hus, _ 1I

U

\hf PI udit be rfsistcd`f is ](bha).

3 bha; Bd cppnyidm c p. l. be 3 vbnt c`rbss thf `bdlu`tbr, ie bdf capcrf urrfdt enbws thrbumh it, thf

rfsistcd`f be c wirf is scil tb of 3 bha.

Ecinurf be Bha's Ncw

3. Luf tb kbunf's Feef`t, thf id`rfcsf id urrfdt cusfs cd id rfcsf id tfapfrcturf id thf bdlu tbr. Hfd f0thf rfsistcd`f id thf wirf id thf wirf id`rfcsfs. \hus, urrfdt lbfs dbt c`tucnny vcry nidfcrny with pbtfdticn

lieefrfd`f. Eim. 3.

Bha's Ncwofidmebnnbwfl

Ecinurf beBha's Ncw

I(Cap)

Eim.3

U(Ubnts)

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@V__FD\ FNF@\_I@I\Y 0

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?. ]hfd c sfai bdlu`tbr liblf is cppnifl with c p. l. c`rbss it, thf cabudt be urrfdt rbssidm thf liblf

lfpfdls upbd thf lirf`tibd id whi`h urrfdt enbws. Id ebrwcrl oicsfl bdlitibd, thf urrfdt thct enbws, is

mivfd oy Eim. ? whfrfcs thf urrfdt thct enbws luridm rfvfrsf oicsidm is shbwd id Eim. 0.

0. Id fnf trbnytfs, thf Bha's Ncw ecins.

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< @V__FD\ FNF@\_I@I\Y

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\hf lriet vfnb`ity be fnf`trbd lfF

va

1 t

rr

)?........(FF

k

dfvC

Ik

lfdsity@urrfdtk

l

s1r

1

11

F 1n

U v

l1

an

fUt

I 1 d C f vl

^ I 1an

tU?dCf

Out, _ 1I

U

_ 1Cdf

a n

t?t1s

t1

a

dfcdl

Fa

dfk

cdlfquctibdsErba

?

?

)?()3(

Cs wf gdbw, _ 1 rCn

r 1t?df

a

0.0 \fapfrcturf Lfpfdlfd`f be _fsistivity; \hf rfncxctibd tiaf tlf`rfcsfs with thf id`rfcsf idtfapfrcturf. \hus, cd id`rfcsf id thf tfapfrcturf winn rfsunt id himhfr rfsistivity be thf actfricn be thf

`bdlu`tbr. \hfrf crf twb ebraucn, whi`h fxpncid this rfnctibd;

( )W Q::373

\\-c+r1rt

r rt _\

0.< Lfpfdlfd`f bd Actfricn ; \hf db. be erff fnf`trbds pfr udit vbnuaf is 'd' cdl it vcrifs erba actfricn.

\hf rfsistivity be thf bdlu`tbr cnsb lfpfdls upbd thf actfricn.

d

3r

0.6 @bdlu`tcd`f cdl @bdlu tivity; @bdlu`tcd`f is lfeidfl cs thf rf`iprb`cn be rfsistcd`f be thf actfricn.

It is rfprfsfdtfl oy M. \hf PIVdit be bdlu`tcd`f is Bha3Wbr Ahb br ]3br Pifafds (P)Q

_M

31

]hy acdmcdid is usfl id thf`bdstru`tibd be stcdlcrl rfsistcd`f`bin2

Cnnbys su`h cs acdmcdid hcvf vfry himhrfsistivity cdl wfcg lfpfdlfd`f bdthfapfrcturf. Acdmcdid (Cd cnnby be `bppfr,

Di`gfn, Irbd cdl Acdmcdfsf hcs 0: tb

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@V__FD\ FNF@\_I@I\Y 6

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\hf PIudit be bdlu`tcd`f is Bha3a3(br ]3a3br Pifafd a3)

r1s 3

0.= \fafrcturf @bfeei`ifdt be _fsistcd`f

Nft rcdl r:of thf rfsistivity be thf bdlu`tidm actricn ct q@ cdl : @ rfspf`tivfny. \hfd,

)3(: cq+r1r

Actfricn nigf Di`hrbaf fxhioit c vfry wfcglfpfdlfd`f be rfsistivityAcdmcdid cdl bdstcdtcd hcvf siaincr prbpfrtifs

Pid`f,_ 1C

nr , wf cd cnsb writf,

_ 1 _:( 3 + 3cq)

^ c 1q

-

:

:

_

__3

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@V__FD\ FNF@\_I@I\Y =

www.thidgiit.id

U31 I_

37 U

?1 I_

?7 U

01 I_

0

U 1 U3+ U

?+ U

0

I_fq

1 I_3+ I_

?+ I_

0

0?3fq ____ ++1

6. _fsistbrs id Zcrcnnfn

@bdsilfr thrff rfsistbrs _3, _

?& _

0put id pcrcnnfn baoidctibd.

_?

_3

_0

+

U

I

I3I?

I0

C octtfry be FAE F is bddf`tfl c`rbss thf baoidctibd. \hfd

thf urrfdt 'I ' id thf ir`uit cd of

mivfd oy

I 1 I3+ I

?+ I

0

whrf I3, I

? cdl I

0rfprfsfdt thf `urrfdt thrbumh _

3, _

?& _

0

rfspf`tivfny. Out, thf p. l. c`rbss fc`h rfsistbr is U sb,

0?3 _

U

_

U

_

U

_

UI

fq

++11

0?3

3333

____fq++1

Idtfrdcn _fsistcd`f be @fnn; \hf rfsistcd`f beefrfl oy thf fnf`trbnytf be thf fnn tb thf enbw be urrfdt.

It is rfpfsfdtfl oy r. It lfpfdls upbd

(c) Dcturf be fnf`trbnytf (o) Listcd`f oftwffd fnf`trblfs

(`) Crfc be fnf`trblf (l) @bd`fdtrctibd be fnf`trbnytf

FAE(Fnf`trbabtivf Ebr`f) ; \hf p. l. c`rbss thf tfraidcns be c fnn whfd db urrfdt u ofidm lrcwd oy

thf ir`uit. It is lfdbtfl oy F. PI udit is vbnt.

_fnctibd oftwffd FAE (F) & (U)

\hf FAE is mivfd oy , F 1 I(_ + r)

^r_

FI

+1

whfrf r is thf idtfrdcn rfsistcd`f be thf fnn.

_r_

FU

+

1

U(_ + r) 1 F_ Ur 1 (F U)_

_U

UFr

-1

3 Ubnt; \hf FAEbe c fnn is bdf Ubnt, ie bdf Kbunf be wbrg is pfrebrafl oy thf fnn tb lrivf bdf @bunbao

be hcrmf rbudl thf ir`uit.

Mrbupidm be @fnns

@fnns id Pfrifs; @bdsilfr d `fnns be FAE F cdl idtfrdcn rfsistcd`f r.

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8 @V__FD\ FNF@\_I@I\Y

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FF F

rrr

_

@fnns id Pfrifs

I I

Ebr lieefrfdt fnns id sfrifs,

Ebr lieefrfdt fnns id pcrcnnfn,

( ) _rrrFFF

I++++

++1

+

.......0?3

.........0?3

...........??

33 ++1

rF

rF

r

F

fq

fq

\hfd thf tbtcn FAE 1 dF

\hf tbtcn rfsistcd`f 1 dr + _

Hfd`f, urrfdt id thf ir`uit,dr_

dFI

+1

Ie but be d fnns, a fnns crf mrbupfl id rfvfrsf brlfr thfd, dft FAE 1 dF(?a)F

@fnns id Zcrcnnfn ; @bdsilfr a rbws be `fnns be FAE F cdl idtfrdcn rfsistcd`f r.

\hfd thf FAE 1 F

\hf tbtcn rfsistcd`f 1 _a

r+

Hfd`f, urrfdt id thf ir`uit,

a

rE

FI

+1

_

r

r

r

@fnns id Zcrcnnfn

F

F

F

^ra_

aFI

+1

Ie r >> _,

_

FI1

Id brlfr tb id`rfcsf urrfdt, thf fnns shbunl of bddf`tfl id pcrcnnfn.

Aixfl Mrbupidm be @fnns

@bdsilfr a rbws be fnns with d `fnns id fc`h rbw hcvidm cd FAE F cdl idtfrdcn rfsistcd`f rid sfrifs id

fc`h rbw. \hfd,

_

F F F

F F F

F F F

Dft FAE 1 dF(FAE be bdf rbw)

Idtfrdcn rfsistcd`f be bdf rbw 1 dr

^ Idtfrdcn rfsistcd`f be a rbws 1a

dr

^ Idtfrdcn rfsistcd`f be thf `ir`uit 1a

dr+_

Hfd`f,

a

dr_

dFI

+1

5. FNF@\_I@CN AFCPV_FAFD\P

Gir`hbee's Ncw ; It bdsists be twb ncws;

Gir`hbee's urrfdt Ncw (Kud`tibd _unf);

\hf cimforci` sua be urrfdt afftidm ct c kud`tibd id cd

i3

i?

i0i