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7/24/2019 Formule Iz OE-I i II-ozujak 2014
http://slidepdf.com/reader/full/formule-iz-oe-i-i-ii-ozujak-2014 1/14
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 BorićLipanj, 2000. O!"in
O#!ja$, 20%&. o'ine
7/24/2019 Formule Iz OE-I i II-ozujak 2014
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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% $ $3 44 Sm/mm2 i %e#% 62 Sm/mm2.
2
7/24/2019 Formule Iz OE-I i II-ozujak 2014
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%4. E"e$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
3
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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$*i' 4
5
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tran*<orator*$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 # )
6
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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' )
7
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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
8
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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
−−−−⋅=⋅−=⋅−==
9
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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
10
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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
76. Kopen1a3ija ja"oe *nae ( -L@tanϕ%, #e"jena ja"oa *naa -@tanϕ2) ,potrena $apa3itina ja"oa *naa C ⋅(3$*ϕ1 - 3$*ϕ2)
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76. Kopen1a3ij*$i $apa3itet C ( $ m%e& U220V; 5'0H %i+e7i
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U
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77. G!ita$ napona na o'! ϕ χ
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79. ;naa !ita$a na o'!22
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90. G!i3i ! *it$! * <eroaneti+no je1ro - #$k$%22 I
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= ;
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i+e7& 3 +e 5$*i *$*; 7k +e k7 3%k&3$ 3 i*i+ki *$*. C QC 22=
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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&.
%5. $+e3*ik 87%$k B%i
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