Enviado por Do utilizador6931

UP0006 CORRENTE ALTERNADA

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JD217. A20.< /.< . 1SA5<. 45 :.14D7.<56JD5 :.<72A . :2A>. A281L70:.
+D214. 2 56>0<2 :.1701D2 2 <.42< 27L .:D>2< 2 >.60BC. 01;5<62 Z >.60BC. 45 >2<7042H
;20 :.<7214. DA A51.< 1SA5<. 45 3
01P26 45 /.<B2 27L . 65D >3
21. 65 406>.<
>5<>5140:D3
2<A5175 Z6<5/5<04263
01P26H 450N214. 45 65< 6545 45 / 5 A 014D?042
CENFIM
15
08
08 #
<.4DBC. 45 / 5 A 601D6.0423:.A 4563
.:2A517. 45 *$Y
5 A 601D6.0423><.4D?042 :.A 4563
.:2A517. 45 *$Y2 ($Y
>2<70< 45675 A.A517.H . 651704. 42 / 5 A 014D?042 12 56>0<2 L:.17<=<0. 2. 2175<0.<
. 517217.H 5 2 A51.64. 651704.H 7D4. 65 >2662 4. A.4. 456:<07.
270185 DA ;23
.< A=N0A. 2>962 <.72BC. 45
/ 5 A 014D?042
'$YH :.A5B214. 2 40A01D0< 27L65 21D3
2<
JD214. . >3
21. 42 56>0<2 65 :.3
.:2 >5<>5140:D3
2<A5175 Z63
01P2645 /.<B2 4. :2A>.
P.A.8L15.H . JD5 6D:545 2>96DA2 <.72BC. :.A>3
572H ;.3
7214. Z>.60BC.
08 &
CENFIM
5 A .I7042 >53
2 <.72BC. 517<5 ($Y5 &$Y
16
.< :242 <.72BC. 42 56>0<2 .I75< 65 = DA2 601D69045
2A>3
07D45 42 / 5 A .I7042
65<= 7217. A20.<H JD217. A20.< /.< . 1SA5<. 45 56>0<26 JD5 :.16707D0 . 014D?04.
.80:2A5175H 2 /<5JDG1:02 45>5145<= 42 ;53
.:04245 45 <.72BC.H
456:<0BC. JD5 2:2I2A.6 45 5/5:7D2< :.14D?0<= 2.6 A56A.6 <56D3
724.6 65 28.<2
406>D65<A.6 45 DA <97.< E
>2<75 A9;53
F :.16707DO
4. >.< DA O
A21 E
53
5:7<.O
A21
23
0A51724. 5A :H:HF 5 DA 567=7.< E
>2<75 /0N2FH :.16707DO
4. >.< I.I0126.145 ;C. 6D<80<
26 / 5 A 014D?0426H >.< A.;0A5172BC. 4. <97.<
><.4D?0< :.<<5175 23
75<1242 601D6.0423
H :P2A2 65
08 '
4.
. 406>.6070;. 456:<07.H :2>2? 45
:
- 5
;
<.4DBC. 45 DA2 8<2145?2 601D6.0423
(
;
.
5 2123
062<A.6 2 5N>5<0G1:02 45 ;5<0/0:2BC. 42 50 45 PA A26 2>3
0:214. 28.<2
8<2145?2623
75<12426H :P582<5A.6Z:.1:3
D6C. JD5 65 A217LA :.1672175 . JD.:05175
%
5675 JD.:05175 :P2A2<5A.6 , ! >57, 4. :0<:D07.H 2. JD232>3
0:2A.6 2
7516C. 23
75<1242 5 JD5 65 <5><565172 >.< &
6D2 D104245 L.I;02A5175 . M
660AH 2 . ,
M
266DA5 2 /.<A2H JD5 L456081242 >.< 50 45
PA 8515<23
0?242
@ &;
40/5<51B2 517<5 & 5
45;5 65 2. /2:7. 45 & 45>5145< 42 /<5JDG1:02
660AH 5A
:.<<5175 23
75<1242H 2 <53
2BC. 517<5 2 7516C. 5 2 :.<<5175 45>5145H >2<2 DA2 4242
/<5JDG1:02H 42 0A>54K1:02 & 5 4. K18D3
. 45 456/262A517. ϕ
.< 45/010BC. 4560812< 65 [email protected]
:.6ϕ
>.<
, -D57,
651ϕ
>.<
7->57, N
CENFIM
17
08 (
<0K18D3
. 4260A>54K1:026
58D042A5175 567D42<5A.6 .6 :0<:D07.6 5A JD5 6D<85A :.<<51756 23
75<12426
601D6.04206H JD5 6C. /.<A24.6>.< <56067G1:026H I.I01265 :.1451624.<56
5<5A.6H 1. 517217.H 5A ><0A50<. 3
D82<H .6:0<:D07.6045206H .D 65R
2H .6:.16707DO
4.6
>.< <56067G1:026H >.< I.I0126>D<26E
65A <56067G1:02F 5 >.< :.1451624.<56>D<.6E
65A
<56067G1:02645 >5<426F
23:.A. 6D:545 12 <523
04245
. 517217.H 23
8DA26 456726 7<G6 8<2145?26H JD5 /.<A2A .6 53
5A517.6 <5206
E
<56067G1:02H <52:7K1:02 014D70;2 5 <52:7K1:02 :2>2:070;2FH 266DA5A ;23
.<567C. I20N.6
JD5 >.45A 456><5?2< 65 /2:5 2.6<56721756
T. :26.H >.< 5N5A>3
.H 4263
KA>242645 01:21456:G1:02H JD5 >.45AH 65A 8<2145 5<<.H
65< :.16045<2426:.A. <56067G1:026>D<26
(
. 2>3
0:2<A.6DA2 7516C. 23
75<1242 601D6.0423Z<56067G1:02 >D<2A5175 9PA0:2H
JD2365<= 2 /.<A2 45 .142 42 :.<<5175 1. :0<:D07.[
>3
0:214. 2 50 45
PA 2.66D:5660;.60167217565 DA2 ;5?JD5
V
HR
= JD5 2
<52:7K1:02 L1D3
2H /2:03
A5175 65 ;5<0/0:2 [email protected]
\ A54042 JD5 2 7516C. 2DA5172H 2 :.<<5175 72AILA . /2<=H R
= JD5 65
<53
2:0.12A >53
2 50 45
PAH
V
Q
+D214. 2 7516C. 2>3
0:242 AD42 45 >.3
2<04245H 72AILA 2 01751604245 45
:.<<5175 AD42 45
CENFIM
5-,
;
18
08 *
56067G1:02 >D<2 23
0A517242 5A
.8. 26:D<;26<5><56517270;2642 7516C. 5 42 :.<<5175 567C. 5A /265H .D65R
2H 2
DA A=N0A. 42 7516C. :.<<56>.145 2 DA A=N0A. 45 :.<<5175H . A56A.
6D:54514. >2<2 .6?5<.6
K 6M ,7
. 65< 3
08242 2 DA2 <545 45 :.<<5175 23
75<12 D12 <56067G1:02 E
> 5N D12 3
KA>242
45 01:21456:G1:02FH 2 01751604245 45 :.<<5175 JD5 :0<:D3
2 75A 2 A56A2 /.<A2
601D6.0423JD5 2 7516C. 42 <545 +D214. 2 7516C. >2662 >53
. ;23
.< ?5<.H 15675
01672175 1C. :0<:D3
2 :.<<5175 E
6D2 01751604245 L?5<.F +D214. 2 7516C. 23
:21B2
. ;23
.< A=N0A.H 2 01751604245 L08D23
A5175 A=N0A2
0?65 517C. JD5 2 7516C.
5 2 01751604245 567C. 5A /265 E
/08 *F
. :26. 45 :2<826 9PA0:26H 2 7516C. 5 2 01751604245 45 :.<<5175 ;2<02A
60AD3
72152A5175
08 $
CENFIM
516C. 5 01751604245 5A /265
19
(
(
6 I.I0126 567C. ><5651756 5A 7.4.6 2JD53
56 <5:5>7.<56 1.6 JD206 65R
2
15:566=<0. 2 ><.4DBC. 45 DA :2A>. A281L70:.
.< 5N5A>3
. 1.653
5:7<.O
A2156H
:.172:7.<56H A.7.<56H <52:7K1:026 45 2<<21JD5 45 3
KA>2426 45 456:2<82
E
/3
D.<56:51756H ;2>.< 45 A5<:S<0.H ;2>.< 45 6940.H 57: FH 7<216/.<A24.<56H 57:
2<2 . 567D4. 4. :.A>.<72A517. 42 I.I012 45;5A.6 75< 5A :.172 JD5 26
I.I01266C. 45 :.I<5H >.< 066. 2><565172<5A DA2 4575<A01242 <56067G1:02
7
5-
7 5-C
5+
53
082<A.6D12 I.I012 2 D12 7516C. :.17O
1D2H :0<:D3
2<=
>.< 53
2 DA2 :.<<5175 53
L:7<0:2 JD5 65<= D10:2A5175 3
0A07242 >53
2 <56067G1:02
58D14. 2 3
50 45
[email protected]
@
%
24. JD5 5672 <56067G1:02 65< >5JD512H 5 65
2>3
0:2A.6D12 7516C. 53
5;242 ZI.I012H :0<:D3
2<= >53
2 A56A2 DA2 :.<<5175 :.A
DA2 01751604245 53
5;242H . JD5 .<08012<= DA2 /.<75 >.7G1:02 40660>242H JD5
>.45<= 4567<D0< 2 I.I012 45;04. 2. :23
.< 85<24.
7
5-
:
- 5
53
082<A.62 A56A2 I.I012 2 D12 7516C. 23
75<12H >.45
65 :.A><.;2< 5N>5<0A51723
A5175 JD5 2 :.<<5175 JD5 :0<:D3
2 >53
2 A56A2
2><565172 DA ;23
.< A51.<
5 3
082<A.6 DA ]277O
A57<. >.45<5A.6 :.A><.;2<
JD5 . :.16DA. 45 >.7G1:02 L ><270:2A5175 1D3
.H 2>562< 42 5N067G1:02 45 D12
:5<72 :.<<5175
660A >.45<5A.6 :P582< Z :.1:3
D6C. JD5 2 I.I012 2><565172
DA2 :5<72 .>.60BC. = >266285A 42 :.<<5175 40/5<5175 4. :26. 2175<0.< 5A JD5 2
.>.60BC. 5<2 45;042 Z<56067G1:02 .PA0:2
.4.656756/519A51.645;5A 65 2. 5/507. 45 2D7. 014DBC. 42 [email protected]
+D214. 2 I.I012 L>5<:.<<042 >.< DA2 :.<<5175 23
75<1242H 2>2<5:5 DA2 :.<<5175
;2<0=;53
H 5 >.< 7217. DA :2A>. A281L70:. 72AILA ;2<0=;53 24. JD5 263
01P26
45 /.<B2 4. /3
DN. A281L70:.H JD5 53
2 A56A2 85<2H :.<72A 2 6D6 ><9><0.6
:.14D7.<56H 6D<85 D12 / 5 A 45 2D7. 014DBC. JD5H 658D14. 2 3
50 45 51?H 65 ;20
.>.< Z:2D62 JD5 3
P5 45D.<085A
08
/ 5 A 45
2D7. 014DBC. 42
I.I012 .>M5 65 Z
:.<<5175
CENFIM
20
+D214. 2 :.<<5175H 658D014. 26;2<02BM5642 /D1BC. 601D6.0423
H 75145 2 :<56:5<H
. :2A>. A281L70:. 72AILA :<56:5
>2<5:5 517C. DA2 / 5 A
JD5 65 .>M5 2 JD5 2 :.<<5175 65 5672I53
5B2H
><.;.:214. DA 27<26. 12 :.A5175 53
L:7<0:2 5A <53
2BC. Z 7516C. E A2 I.I012
2. 65< 3
08242 2 DA2 7516C. 23
75<1242H 2 7516C. 2>2<5:5 45 0A54027. 2.665D6
75<A01206F
K ,5 +-,9
5 2 DA2 <545 45 :.<<5175 23
75<12 /.< 3
0824. DA <5:5>7.< 014D70;.H ;20 42<
.<085A 2 DA 456/262A517. 517<5 2 7516C. 5 2 01751604245
672 S3
70A2H 5A
;0<7D45 42 2D7. 014DBC.H 5672<= 27<26242 5A <53
2BC. Z7516C.
675 456/262A517.H :.A. 7.4. . K18D3
.H >.45 65< A5404. 5A 8<2D6
. :26. 45
D12 :2<82 014D70;2 >D<2H 5A JD5 <56067G1:02 9PA0:2 L1D3
2H . 456/262A517. 65<=
45 *$^
. :26. 45 :2<82 014D70;2 >D<2H 2 01751604245 45 :.<<5175 5175 27<26242 *$^E
45 >5<O
.4.F 5A <53
2BC. Z7516C.
08
CENFIM
028<2A2 ;5:7.<02345
5
1DA2 I.I012 >D<2
21
5675 :26. 40?65 JD5 2 01751604245 567= 456/26242 5A 27<26. 5A <53
2BC. Z
7516C. 5A DA JD2<7. 45 :0:3
.
O
(
.A. 2 .>.60BC. 2><56517242 >53
2 I.I012 Z:.<<5175 23
75<1242 75A 2 ;5< :.A .6
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672 65<= A20.< JD217. A20.< 65R
2 . :.5/0:05175 45
2D7. 014DBC. .?5 A206<=>042665R
2A 26;2<02BM5642 :.<<5175 23
75<1242
2 I.I012 Z
P2A2A.6 <52:7K1:02 014D70;2 N. Z .>.60BC. 2><56517242 >53
:.<<5175H >53
. [email protected]
X L = 2πfL
- V
52:7K1:02 014D70;2 5A .PA6EΩ F
/ V <5JDG1:02 5A P5<7?E
!?F
V
.5/0:05175 45 2D7. 014DBC. 5A P51<06E
!F
P
(
23:.A. 0140:=A.62. ><01:O
>0. 45675 75A2H A545 65 2 >.7G1:02 45 DA2 I.I012
>D<2H >.45 65 :.A><.;2< JD5 2 3
507D<2 27<2;L6 45 DA ]277O
A57<. 0140:2 DA2
>.7G1:02 08D232 ?5<.
. :.17<=<0. 4. JD5 .:.<<5 1DA2 <56067G1:02H 1DA2 I.I012 >D<2 1C. 65 ><.4D?
151PDA :.16DA. 45 515<802 :23
.<O
/0:2
:.<<5175 JD5 >5<:.<<5 2 I.I012 65<;5 D10:2A5175 >2<2 85<2< . :2A>.
A281L70:.
2 <523
04245 . JD5 .:.<<5 L JD5H 2. :<56:5< 2 :.<<5175 >53
2 I.I012H 72AILAH
2:.175:5 . A56A. 2. :2A>. . :2A>. A281L70:.H ><.4D?014. 65 DA :.16DA. 45
515<802 53
L:7<0:2
5675 :26. 2 515<802 /3
S0 4. 85<24.< 27L Z I.I012 5 L JD214.
40?5A.6JD5 5672 567= 2 :.16DA0< 515<802 53
5:7<.A281L70:2
A2 ;5?23
:21B242
2 :.<<5175 A=N0A2 5 . /3
DN. A=N0A.H 56756 75145A 2 40A01D0< 658D014. 2
7<2R
5:79<02 601D6.0423
H 45651<.3
214. 65 DA2 / 5 A 45 2D7. 014DBC. 45 723651704.
JD5 85<2 DA2 515<802 53
L:7<0:2 JD5H 28.<2H /3
S0 45645 2 I.I012 27L 2. 85<24.<
5675 :26.H 2 I.I012 45;.3
;5 2 515<802 2. 85<24.<
5672 A2150<2 40?5A.6JD5 2
I.I012 1C. :.16.A5 <523
A5175 2 515<802H A2660A>3
56A5175 2 7.A2 5A><567242
4D<2175 DA JD2<7. 45 :0:3
. >2<2 85<2< . 65D :2A>. 53
5:7<.A281L70:.H >2<2 2
45;.3
;5< 1. JD2<7. 45 :0:3
. 658D0175
CENFIM
22
24. JD5 . ]277O
A57<. A545 . ;23
.< AL40. 42 >.7G1:02 5 5672 L6 >.6070;2
4D<2175 DA JD2<7. 45 :0:3
. 5 158270;2 1. 658D0 175
675 1C. 0140:2 151PDA2
>.7G1:02
660A 2 I.I012 1C. :.16.A5 515<802
6 :.16721756 :2<826 5 456:2<826 42
A56A2 .<08012A :.A JD5 5 :0<:D3
5 DA2 4575<A01242 :.<<5175 1.6:.14D7.<56H
>.< 7217.H 72AILA 2>2<5:5 DA2 >.7G1:02H 2 JD5 :P2A2<5A.6>.751:02 <52:70;2
E
+2
+
, 7+,-
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L @ N.
$
1
2 19 :
-
!
7-,9 2
.
A2 I.I012 <5232><565172 <56067G1:02 9PA0:2 45;04. Z6D2 :.16707D0BC.
Z = R 2 + X L2
08
.I012
660A >.45A.6 .I75< DA :0<:D07. 04G170:. 2. 42 /08D<2
:.16045<2< . ;23
.< 42 <56067G1:02
5675 :26. 45;5<5A.6
5 . 42 <52:7K1:02 014D70;2 N. 65>2<24.6
08
CENFIM
23
. :0<:D07. 014D70;. 2 :.<<5175 27<26242 45 DA K18D3
.
. :26. 4. :0<:D07.
ϕ
5A <53
2BC. Z7516C.
H . 456/262A517. ;2<02 517<5 $Y5 *$Y
P
08 #
S=U.I
(VA)
P = UR . I = U . I COS ϕ
(W)
QL = XL . I = U . I SEN ϕ
(VAr)
.7G1:0261DA2 I.I012
'
(
(
6:.1451624.<561C. 6C. <5:5>7.<56JD5 65R
2A D703
0?24.6P2I07D23
A5175 :.A.
26 <56067G1:026 5 26 I.I0126 . 517217. 6C. AD07. S7506H >.< 5N5A>3
.H >2<2
:.17<2<02< .6 /519A51.6 158270;.6 JD5 ><.4D?5A 26 >.7G1:026 <52:70;26 426
I.I0126
7
5- 7 5-,5+ H 69 :0<:D3
2<= :.<<5175 53
L:7<0:2 >53
. :0<:D07. 4D<2175 2
:2<82 4. :.1451624.<
5672 /.<A2H >.45 65 40?5< JD5 DA :.1451624.< 1C.
>5<A075 2 >266285A 42 :.<<5175 :.17O
1D2
7
5:
- 5
H . :.1451624.< /0:2<= :2<<5824. 23
75<1242A5175
>5<A07014. 2660A :.<<5175 1. :0<:D07.
CENFIM
24
08 &
028<2A2 ;5:7.<02345
5
1DA :.1451624.<
:2<82 :2>2:070;2 E
:.1451624.<FH JD214. 0165<04. 1DA :0<:D07. 45 :.<<5175
23
75<1242 .<08012 DA 456/262A517. 517<5 7516C. 5 01751604245
:.<<5175
2>2<5:5 5A 2;21B. 5A <53
2BC. Z7516C.
. :26. 42 :2<82 :2>2:070;2 >D<2H 2 01751604245 45 :.<<5175 2402172 *$^E
45
>5<O
.4.F 5A <53
2BC. Z7516C.
O
(
A :.1451624.<H 5A
H >5<A075 JD5 /3
D2 :.1672175A5175 DA2 :.<<5175
53
L:7<0:2 >53
. :0<:D07. 45;04. Z6 :.16721756H :2<826 5 456:2<826 4. A56A. T
0A>.<72175 1.72< JD5 5672 :.<<5175 5+57
75
5
P2A2A.6
-
9
, :
)7- ,7
H A2660A >53
.6:.14D7.<564. :0<:D07.
7->57,
7 ! 7,-,9
75
5
N
Z .>.60BC. JD5 .
:.1451624.< 2><565172 Z:.<<5175
-: V
52:7K1:02 :2>2:070;2
5A .PA6
1
XC =
2πfC
/ V <5JDG1:02 5A P5<7?
V
2>2:04245 4.
:.1451624.< 5A /2<246
08 '
P
52:7K1:02 :2>2:070;2
(
8D232. JD5 .:.<<5 :.A 2 I.I012H 65 /.< A54042 :.A DA ]277O
A57<. 2 >.7G1:02
45 DA :.1451624.<H >.45 65 :.A><.;2< JD5 2 >.7G1:02 0140:242 L08D232 ?5<.
DA :.1451624.< 1C. 5N0675 :.16DA. 45 515<802 2:70;2
JD2<7. 45 :0:3
. . :.1451624.< L 7
CENFIM
K
7
5
K,
D<2175 . ><0A50<.
:
)7- ,7
E
25
7 K
:7-
:.1451624.<
-8-,7 H >53
. JD5 2 515<802 /3
S0 4. 85<24.< 45
>2<2 .
. JD2<7. 45 :0:3
. 658D0175 . :.1451624.< 456:2<<582 >2<2 .
:0<:D07. 27L2. 85<24.<H 45;.3
;514. 2. A56A. 2 515<802 2:DAD3
242
2AILA 2>2<5:5 D12 >.7G1:02 <52:70;2 L7><.4D?042 >53
2 515<802 JD5 L7<.:242
517<5 . :.1451624.< 5 . 85<24.<
DA :.1451624.<@ +: V -:
08 '
E
F
E;.3
7 2A>5<5 <52:70;.6F
0<:D07.
5675 :26. . 456/262A517. ;2<02 517<5 $^5 *$^E
/08 'F
R = Z COS ϕ
XC = Z SEN ϕ
Z2 = R2 + X2C
UR = U COS ϕ
UC = U SEN ϕ
U 2 = U R 2 + U 2C
S = U . I (VA)
P = U .I . cos ϕ (W)
QC = U .I . ses ϕ (VAr)
S2 = P2 + Q2C
08 (
CENFIM
26
.
5 3
082<A.6 DA2 <56067G1:02H DA2 I.I012 5 DA :.1451624.< .I75A.6 DA
7, 7+,-
. ;
08 *
0<:D07.
5675 :26. 2 0A>54K1:02 4. :0<:D07. ;[email protected]
Z2 = R2 + X2
Z2 = R2 + (XL – XC)2
X L = 2πfL
XC = −
1
2πfC
X = 2πfL −
1
2πfC
+D214. - V $H E
- V - FH P= <566.1K1:02 1. :0<:D07.
5675 :26. 2 0A>54K1:02 4. :0<:D07. L08D232
V
08 $
CENFIM
27
;
H
P
(
P
.
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41
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P
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b
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V
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3 UC IL sen ϕ
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P=
CENFIM
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2<82 014D70;2 2175642 :.<<5:BC.H
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58
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ELECTROTECNIA-TEÓRICA E APLICADA, (ÁLVARO BADONI - PORTO EDITORA)
ELEMENTOS DE ELECTRICIDADE, (SIMÕES MORAIS - PORTO EDITORA)
ELECTROTECNIA – PROBLEMAS E ITENS (DIDÁTICA EDITORA-JOSÉ VAGOS
MATIAS)
ELECTROTECNIA – PROBLEMAS E ITENS – 2 (DIDÁTICA EDITORA-JOSÉ VAGOS
MATIAS)
CATÁLOGO GERAL-91 (MERLIN GERIN)
ELECTROTECNIA (PARANINFO-PABLO ALCADE SAN MIGUEL)
CENFIM
60
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