Formule Iz OE-I i II-ozujak 2014

14
OBRTNIČKA I TEHNIČKA ŠKOLA OGULIN O S N O V E E L E K T R O T E H N I K E F O R M U L E I K O N S T A N T E (repetitorij)  prof. Zdravko Borić Lipanj, 2000. O!"in  O#!ja$, 20%&. o'ine  

Transcript of Formule Iz OE-I i II-ozujak 2014

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OBRTNIČKA I TEHNIČKA ŠKOLA OGULIN

O S N O V E E L E K T R O T E H N I K E

F O R M U L E I K O N S T A N T E

(repetitorij)

prof. Zdravko BorićLipanj, 2000. O!"in

O#!ja$, 20%&. o'ine

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or!"e i $on*tanteOSNOVE ELEKTROTEHNIKE I i II

%. E"eentarni e"e$tri+ni naoj e≈

1.6⋅

10-19 C

2. Ko"i$o naoja ia ! ne$o naoj! -() NeQ N =

/. E"e$tri+na (o!"ooa) *i"a F2

21

d

QQk F ⋅⋅= (N)

&. Kon*tanta o!"ooe *i"e 1a 1ra$ k≈

9⋅

10 9 (Nm2 /C2)

. E"e$tri+ni poten3ija" ! to+3i BϕB )( V

As

VAs

Q

W B B ==ϕ

4. E"e$tri+ni napon i1e5! to+a$a A i B UAB ϕB - ϕA (V)

6. Napon i1e5! 'ij! to+a$a UBA Q

W

Q

W W

Q

W

Q

W U A B A B

A B BA

∆=

−=−=−= ϕ ϕ

7. 8a$o*t *tr!je I )( A s

As

t

Q I ==

9. G!*to:a *tr!je ! )10(2

3

2 mm

A

m

A

s

I J ⋅==

%0. E"e$tri+ni otpor R )(Ω⋅= s

l R ρ

%%. ;pe3i<i+ni otpor ρ

)(2

mm

m

l

s RΩ=

⋅Ω⋅= ρ

%2. 8e'ini3a 1a *pe3i<i+ni otpor $o' ra1"i+iti= aterija"a>

- otporno*t o'i+a [ ] ( )mmmm ⋅Ω=

⋅Ω= −6

2

10 ρ

- otporno*t i1o"atora [ ] ( ) ( )mcmcm

cm⋅Ω=⋅Ω=

⋅Ω= −2

2

10 ρ

- otporno*t (*pe3i<i+ni otpor) t"a [ ] ( )m⋅Ω= ρ

%/. E"e$tri+na o'"jio*t ")

1(

11 1 S l

s

s

l RG =Ω=

Ω⋅=

⋅== −

ρ ρ

%&. ;pe3i<i+na o'"jio*t χ

)1010(11

2

62

mm

S

cm

S

m

S

s R

l

l s R

−− ==

=

== ρ

χ

%. Kon*tanta ? @roo'no*t i"i *pe3i<i+na o'"jio*t aterija"a $oji *e naj+e:e$ori*te! e"e$trote=ni3i> - #$k$% C& '6 Sm/mm2 - $&mi*i+ A ,' Sm/mm2 - e+e Fe 10 Sm/mm2 - $m %im+e% $ $3 44 Sm/mm2 i %e#% 62 Sm/mm2.

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%4. E"e$tri+na o'"jio*t o'i+a "l

sG ⋅= χ

%6. @rojena otpora ra1jerna i projeni teperat!re R 20 R R ⋅∆⋅=∆ ϑ α

%7. Teperat!rni $oe<i3ient α

Ω

Ω

⋅∆

=

K R

R 11

20 ϑ

α

%9. e<ini3ija> Teme%$3&%*i ke5iie*3 +e7*$k +e %m+e*i 1Ω

3%$ %i

%m+e*i 3eme%$3&%e 7 1 K. 8$ e :i3e me3$e 3eme%$3&%*i ke5ii+e*3 +e %i#i* +e7*$ke ei:i*e i 3 k 0;4< 1K 7** 10 C.

20. Teperat!rna oi*no*t otpora Rυ

( )[ ]20120 −⋅+⋅= ϑ α υ R R

2%. Teperat!rne oi*no*ti α ne$i= aterija"a (K?%) ? e 0,00&4 'o 0,0042 ? 3in$ 0,00&2 ? Ko*itar 0,00&4 ? o"<ra 0,00&%

? o"oo 0,00&2 ? 1"ato 0,00&0? p"atina 0,00&0 ? #$k$% 0;00,9

- $&mi*i+ 0;00,= - *rero 0,00/7 ? ni$a" 0,00/6 'o 0,004 ? je' 0,00%

? $on*tantan ± 0,0000& ? !"jen ? 0,0007

22. O>m $k*

)( )( )(

)( )( )(

S U

I GV

G

I U AU G I

I

U RV R I U A

R

U I

==⋅=

Ω=⋅==

2/. Kir3==o<<o 1a$on 1a napone ($?e#$%ki #%+ *$*$ &7& $3%e*e

e3+e eek3%i:*? k%&?$ +e7*$k +e *&i.)2&. U$!pni otpor *erij*$o *poja otpora R&k R1 @ R2 @ R, @ R4 @... @ R*

2. Kir3==o<<o 1a$on 1a *tr!je ($?e#$%ki #%+ 3%&+$ & #i k++ 3:kieek3%i:*? k%&?$ +e7*$k +e *&i.)

24. U$!pni otpor para"e"no *pojeni= otporanuk R R R R R R

1...

11111

4321

+++++=

24. U$!pni otpor 'aj! para"e"ni= rana R&k 21

21

R R

R R Ruk +

⋅=

26. U$!pni otpor n *pojeni= je'na$i= otpora R&kn

R Ruk =

27. E"e$tri+na enerija U⋅

(I⋅

3) U⋅

I⋅

3 (V A⋅

VA)

29. E"e$tri+na *naa )( W VA I U t

t I U

t

W P =⋅=

⋅⋅==

/0. ;naa na otpor! )(22

W R I R

U P ⋅==

/%.Top"in*$o 'ije"oanje e"e$tri+ne *tr!je

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/&. 8e'na'#a i1ora U U0 - I ⋅ Ri

/. Un!tarnji otpor i1ora Ri k

i I

U R 0

/4. Oi*no*t *nae troi"a o otpor! troi"a t

t i R R R

U P ⋅+= 2

2

0

)(

/6. @ri"ao5enje *nae i1ora na*t!pa R3 Ri

/7. Naje:a *naa $oj! i1or o#e 'ati troi"! ! pri"ao5enj! m$k

i

i

i

i

ii

maks R

U R

R

U R

R R

U P

⋅=⋅

⋅=⋅

+=

4)2()(

2

0

2

2

0

2

2

0

/9. 8a$o*t e"e$tri+no po"ja E )(m

V

As

m

VAs

As

N

Q

F E ===

&0. G!*to:a e"e$tri+no to$a D )( 22 m

C

m

As

E D =⋅= ε &%. a$tor ra1jerno*ti i"i 'ie"e$tri+na $on*tanta ε

ε0 ⋅ ε%

&2. ie"e$tri+no*t a$!!a i"i e"e$tri+na $on*tantaε0 G;G'

10-12 A/Vm

&2. Ta"i3a re"atini= 'ie"e$tri+ni= $on*tanti ne$i= aterija"a$3e%i+$

ε%

1ra$ %,0004papir %,4...2

tran*<orator*$o !"je 2,2po"i*tiren 2,

po"iini"$"ori' (@C) &,

neopren 6por3!"an ...6

*ta$"o ...%0$arton ,...7tinja3 6

o'a ('e*ti"irana) 7%titan'io$*i' %00

po*ene r*te $erai$e i1na' 00&/. Hooeno po"je$) ?&3$ 3k$ D / #) +$k3 +$ E U / 7 (7-%$m$k :$ >m?e*? +$)

&&. @roojni napon U E ⋅ 7

&&. Ta"i3a 'ie"e$tri+ne +r*to+e Ep ne$i= tari$3e%i+$ E ( kV / mm)

1ra$ /papir /...20

por3!"an titan'io$*i' 4

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tran*<orator*$o !"je %%neopren %%*ta$"o %/

po"i*tiren 2po"iini"$"ori' (@C) /

$arton /0...40po*ene r*te $erai$e 'o /00

&. Kapa3itet C / U ( A/VF)

&4. Kapa3itet p"o+a*to $on'en1atora C )(0 F d E

s E

d E

s D

U

QC

⋅⋅⋅⋅

=⋅⋅

== ε ε

&6. ;erij*$i *poj $on'en1atora 1 2 ... U&k U1 @ U2 @ ... C&k

)(21

21 ak!nden"at! s#!$ena sei$skidva "aC C

C C C uk

+

⋅= ...

!111

321

+++=C C C C uk

&7. O'no* napona i $apa3iteta $o' 'a *erij*$i *pojena $on'en1atora 1

2

2

1

C

C

U

U

=&9. @ara"e"ni *poj $on'en1atora 1 @ 2 U1 U2 U C&k C1 @ C2 0. O'no* $o"i+ine naoja i $apa3iteta $o' 'a para"e"no *pojena $apa3iteta

2

1

2

1

C

C

Q

Q=

%. @ri$"j!+enje $on'en1atora (*erij*$i *poj R i )- *$* *$ R &R i

R U - &C

- *$* *$ C &C %C C

%uC ⋅==

1

- e*e%?i+$ k+& i% 7$+e +& R i C i ⋅

U

- e*e%?i+$ *$#i+e*? k*7e*$3%$ C C

QU C U QW C ⋅

=⋅

=⋅

=222

22

- e*e%?i+$ *$ 3%& R U QU QU QW W W C i R ⋅⋅=⋅⋅−⋅=−=2

1

2

1

- %eme*k$ k*3$*3$ C R ⋅=τ

- 3%&+$ %i *$#i+$*+& k*7e*$3%$ C R

t t

#i$ stac e R

U e I iii ⋅

−−⋅=⋅+=+= τ

00

- *$* *$ 3%& (&*+e*+e) τ

t

R eU Rt it u

⋅=⋅= )()(

- *$* *$ C (&*+e*+e) )1()()( τ τ

t t

RC eU eU U t uU t u−−

−⋅=⋅−=−=

- i#i+$*+e C C R

t t

e R

U e I t i ⋅

−−⋅=⋅= 0

0)( τ

- i#i+$*+e *$* *$ k$$i3e3& i 3%& τ

t

RC eU Rt it ut u−

⋅=⋅== 0)()()(

2. Danet*$a !1!'a (protje3anje)Θ

I⋅

N (A)

/. Danet*$i to$ B⋅

( V # )

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&. G!*to:a anet*$o to$a B )(22

& m

W'

m

sV

s B ==

⋅Φ=

. 8a$o*t anet*$o po"ja H )(m

A

l

I N (

s

⋅=

4. @o"je rano o'i+a Hπ ⋅⋅==Θ=

I l I

l (

2

6. @o"je rano *it$a H )( svitkadul$inal l

I N ( sv

sv

−⋅

=

7. @ereai"no*t µ

)( Am

Vs

(

B= µ

9. @ereai"no*t a$!!aµ0 1;2'=

10 -6 V/Am

40. Re"atina pereai"no*tµ% µ

/µ0

4%. Re"atine pereai"no*ti aterija"a$3e%i+$ m$k.

µ% :e3*$µ%

inao?"i (ne"eirani) /000 %0

inao?"i ("eirani) 400 20Hper %0 000 2 00

Deaper 60 000 / /00@era""o 70 000 4 000

42. O=o 1a$on 1a anet*$i $r!

)(1

)(

)(

Vs

A

s

l R

A

Vs

l

sG

l

s s

l

s B

R

s m

s

m

s s

m

⋅=

⋅=

Θ⋅⋅=⋅Θ

⋅=⋅=Φ

Θ=Φ

µ

µ

µ µ

4/. Fa$on protje3anja N⋅

I H⋅

NI ∑

H

4&. Fa$on protje3anja ( 1ra+ni rapon ! e je1ri ) N I H5e @ H004. ;i"a na o'i+ protje3an *tr!jo F B

I⋅

(N)

44. ;i"a i1e5! 'aj! rani= o'i+a F

))((2

21021 v!dica sedistaa"mak d d

l I I l I B F −⋅⋅

⋅⋅⋅=⋅⋅= π

µ

46. ;i"a na tije"o o' e$o #e"je1a F0

2

2 µ ⋅⋅

= s B

F

47. ;i"a na naoj ! ianj! F vQ Bt vt

Q Bl I B F ⋅⋅=⋅⋅⋅=⋅⋅=

49. In'!$3ija ianje o'i+a ( i1o' )

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? anet*$a *i"a FmB (N)

? prot! e"e$tri+na *i"a FeE

vl Bu

vl Bl E

v B E vQ B E Q F F

i

me

⋅⋅=⋅⋅=⋅

⋅=⋅⋅=⋅=

60. In'!$3ija projeno to$a &i t t

s Bt )l Bvl Bui ∆∆Φ=∆∆⋅=∆∆⋅⋅=⋅⋅=

6%. Fa$on e"e$troanet*$e in'!$3ije &i (F$%$7$Je $k* EI)t

N ui ∆∆Φ⋅−=

62. Na+e"o ra'a eneratora ( )

s B N U

t U t s Bt u

t * s Bt

t s B s B s B

s sa #!vie*ektivna

s Bt!k ma+

m

m

⋅⋅⋅=

⋅⋅=⋅⋅⋅=⋅⋅⋅⋅⋅=Φ

⋅⋅⋅=⋅⋅=⋅=Φ

⋅=

⋅=Φ

ω

ω ω ω

π

ω α

α

)sin()sin()(

)2cos()(

coscos

cossin

..

,

,

,

6/. @ojaa *aoin'!$3ije

t

i ,u

t

i

R

N u

R

i N

t N u

s

m

s

m

s

∆∆⋅−=

∆∆⋅−=

∆⋅=∆Φ

∆∆Φ⋅−=

2

6&. In'!$tiitet

s

m

m

m

m

s s

l

s N ,

I

N

R

N ,

I R

N

R

I N

R

N ,

AVs (

it u

t

iu ,

⋅⋅=

Φ⋅==

Φ=

⋅=Φ

=

=∆∆⋅=

∆∆

=

µ 2

2

2

)(

6. De5!in'!$tiitet ?t

N u - ∆∆Φ⋅−= 12

2

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64. Tran*<orator ? 22

2

2

11

1

2

2

1

2

1

2

1 R N

N R

N

N

i

i

N

N

u

u⋅===

66. ;erij*$i *poj in'!$tiiteta ?t

i ,

t

i , ,

t

i ,

t

i ,u uk uk ∆

∆⋅=

∆∆⋅+=

∆∆⋅+

∆∆⋅= )( 2121

? L&k

L1 @ L

2 @ ...

67. @ara"e"ni *poj in'!$tiiteta -nuk , , , ,

1...

111

21

+++=

69. Enerija *it$a ?2

2 , I W ,

⋅=

70. U$ap+anje i i*$ap+anje RL ? $r!a > - *e%e7* *$k* &k$:$*+$;i*7&i%$*i *$* *$ i*7&k3ii3e3& i*& +e +e7*$k *$*& i%$.

&R U0 - &L i &R / R (U0 - &L ) / R I U0 / R

%eme*k$ k*3$*3$τ

L / R

- Ve i k7 m$*+i> i3$k$ m?& e %i ik$:$*+& +$i3i *$*i 7*ekik ki3i.

- *$* *$ i*7&k3ii3e3& τ

1

)(−

⋅= eU t u ,

- *$* *$ 3%& )1()()( τ τ

t t

, R eU eU U t uU t u−−

−⋅=⋅−=−=

- 3%&+$ )1()(

)( τ τ τ

t t t

R e I e I I e R

U

R

U

R

t ut i

−−−−⋅=⋅−=⋅−==

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7%. U i1jeni+noj *tr!ji $ori*ti *e $op"e$*ni roj. O*noe $op"e$*no roja>

(modul)tvrijdnos!"solutn! #

(v$tor) %roj$om"l$sni

)sin(cos

"is!tismo& 'mjsto

%roj!$om"l$sno

o%li$ j!lni$s"onnciis&ovo%li$do%ivniov!$o

)sin(cos

)sin(cos

sincos

jdi*ulru vri+rm!

o%li$ $ionomtrijs......tri)sin(cos

sincos

#

sin

cos

o%li$ iortoon!lnili "r!vo$utni

j

22

∠==+=+=

⋅=+=+=

+⋅=

±=

+=

+=+=

==

+=

⋅=

⋅=

⇒+=

+

±

.

. .e $ . $/ R .

e

e . $ . $/ R .

$ee

$

$ . .

$. . $/ R .

R

/ act+

R

/ t+

/ R

. /

. R

$/ R .

$

$

$

a $a

ϕ ϕ ϕ

ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ I

ainarni roj i"i iainarna je'ini3a>− = − = − ⋅ = ⋅ =

= =

= − = −

= − = −

= = ∈

− +

+

+

1 4 1 4 2 2

1 1

1 1

1 4 1

2 4 2

3 4 3

4

$ $ $

$ $ $ $

$ $

$ $ $ $

$ k . k

k

k

k

(

j j s$u"

cijli- %rojv!)

4$

7%. 'o'ata$ 20%&> U i1jeni+noj *tr!ji $ori*ti *e $op"e$*ni roj. O*noe

$op"e$*no roja>

R

/ t+

R

/ t+

/ R .

. /

. R

$/ R .

1

22

sin

cos

o%li$ iorto(on!lnili "r!vo$utni

==

+=

⋅=

⋅=

→+=

ϕ ϕ

ϕ

ϕ

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o%li$ "ol!rni )sin(cossincos

o%li$ j!lni$s"onnci )sin(cossincos

)sin(cos

sincos

o%li$ mtrijs$i triono )sin(cossincos j

→∠=⋅=+⋅=+=+=

→⋅=+⋅=+=+=

+⋅=

+=

→+⋅=+=+=

+

ϕ ϕ ϕ ϕ ϕ

ϕ ϕ ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ ϕ ϕ

ϕ

ϕ

ϕ

ϕ

. e . $ . $. . $/ R .

e . $ . $. . $/ R .

$ee

$

$ . $. . $/ R .

$

$

a $a

Iainarni roj i"i iainarna je'ini3a>− = − = − ⋅ = ⋅ =

= =

= − = −

= − = −

= = ∈

− +

+

+

1 4 1 4 2 2

1 1

1 1

1 4 1

2 4 2

3 4 3

4

$ $ $

$ $ $ $

$ $

$ $ $ $

$ k . k

k

k

k

(

j j s$u"

cijli- %rojv!)

4$

72. ;naa i1jeni+ne *tr!je>- %$7*$ *$?$ - $m (:i3i) R. )(

22

W R I R

U I U P ⋅==⋅=

- +$$ k$$i3i*$ )(22

VA / I /

U I U Q C

C

C ⋅==⋅=

- i*7&k3i*$ )(22

VA / I /

U I U Q ,

,

, ⋅==⋅=

7/. ;erij*$i *poj o*$o, $apa3itino i in'!$tino otpora ? !$!pni otpor i"iipen'an3ija 82 R2 @ (L - C)2

7&. Re1onan3ija ? $a' je L ? re1onantna <re$en3ija C , * ⋅⋅⋅= π 2

1

7. @ara"e"ni *poj o*$o, $apa3itino i in'!$tino otpora ? !$!pna o'"jio*ti"i a'itan3ija M2 "2 @ (BC - BL)

2 M1/8 "1/R B1/ (oi*no o L i )74. ;naa i1jeni+ne *tr!je >

- %ii7*$ *$?$ )(22

VA . I .

U I U S ⋅==⋅=

- R$7*$ *$?$ )(coscoscos 22

W . I .

U I U P ϕ ϕ ϕ ⋅=⋅=⋅⋅=

- !$$ *$?$ ϕ ϕ ϕ sinsinsin 22

⋅⋅=⋅=⋅⋅= . I .

U I U Q

- F$k3% *$?eS

P =ϕ cos

- K&3 m$k$ϕ

S

P rccos=ϕ

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76. Kopen1a3ij*$i $apa3itet C ( $ m%e& U220V; 5'0H %i+e7i

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F%m&e e m?& k%i3i3i %i i%$7i 3e3$ *$*+$ i kki> $7$$ 3+ekm kke ?7i*e i 3+ekm +e#i $%i+eme $3$. N$7$m e 7$ ?%ek$ k+& $m &:i*i *i+e *$m+e%*$ i %i$i 7$ i +e e & %e7&.

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